Skeptics and Unruly Connectives:A Defence of and Amendment to the Non-Factualist

Justification of Logic

by

Oliver Oxton

A thesis

presented to the University of Waterloo

in fulfilment of the

thesis requirement for the degree of

Master of Arts

in

Philosophy

Waterloo, Ontario, Canada, 2018

c©Oliver Oxton 2018

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis,

including any required final revisions, as accepted by my examiners.

I understand that my thesis may be made electronically available to the public.

ii

Abstract

This thesis attempts to positively solve three problems in the foundations of logic. If logi-

cal connectives are defined by their introduction and elimination rules, then how might one

prohibit the construction of dysfunctional rules, i.e. rules which let us infer anything from

anything else? How might one be held accountable to the consequences of those logical

rules that they accept in an argument? And, how might one who, for whatever reason,

doubts those logical rules regularly taken for granted, be convinced to adopt deductive

‘best practices?’ A variety of positions in the foundations of logic are reviewed, but it

is found that each either fails to answer all questions together, or leads one to troubling

epistemic conclusions. This thesis attempts to draw broad lessons from those positions

otherwise found wanting, and then builds on the seemingly most plausible perspective;

namely, non-factualism. Particularly, it is argued that non-factualism fails to distinguish

between epistemic values and epistemic domains, and that the consequence of this dis-

tinction allows one to effectively compare the success of their deductive practices with the

skeptic.

iii

Acknowledgements

Dave DeVidi,

Greg Andres,

Nick Ray,

and the University of Waterloo’s Philosophy community, for all their encouragement.

iv

Table of Contents

Introduction 1

1 Rule-Circularity and Conceptual Role Semantics 6

1.1 Meaning As (Almost) Use . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2 Solutions: Better and Worse . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3 The Role of Rule-Circularity . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Logic with an Epistemological Foundation 19

2.1 Problems (Two Different Ones) . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Intellectual Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3 Default Reasonable Beliefs . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.4 The Morals So Far . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3 Logical Methodology and Non-Factualism 42

3.1 A Priori Logic, Weak and Strong . . . . . . . . . . . . . . . . . . . . . . . 43

3.2 Evidence and Contingent Reasoning . . . . . . . . . . . . . . . . . . . . . . 46

3.3 Universal Reasoning and Circular Justification . . . . . . . . . . . . . . . . 51

3.4 The Ups and Downs of Non-Factualism . . . . . . . . . . . . . . . . . . . . 57

4 Non-Factualism+ : An Amendment 64

5 Conclusion 72

Bibliography 73

v

Introduction

Discussions in the foundations of logic all, one way or another, must deal with issues

arising from two short papers: Lewis Carroll’s “What the Tortoise said to Achilles”, and

Arthur Prior’s “The Runabout Inference Ticket”. In the first, Achilles and the Tortoise

discuss the nature of entailment relations through the examination of a modus ponens

argument. Given that one accepts P and P → Q, would it ever be acceptable to refuse

to assent to Q? Must one infer Q whether they like it or not? In the second, a new and

problematic logical connective, Tonk, is introduced. It’s common to think that once one

has given suitable introduction and elimination rules for a logical connective, one has done

everything required to specify its meaning. Certainly, this is the way we often teach logic

to students. Tonk appears to ‘follow the rules’: it has such introduction and elimination

rules, and under certain conditions it can lead us to true conclusions; however, Tonk turns

out to allow us to infer anything from anything else, and so it’s not clear that the initial

rules gave it any sort of meaning at all. The lesson seems to be that one must accept

some restrictions on the sorts of definitions of connectives that are allowed, restrictions

that will have to be specified outside the formal logical system being developed. This,

of course, raises the questions: which principle should be invoked and for what reasons?

Before outlining the structure of the thesis, it will first be of benefit to give further detail

to these guiding issues.

Carroll’s Tortoise, playing the role of the skeptic by accepting both P and P → Q but

refusing to accept Q, leads Achilles to the conclusion that if he were to ever successfully

convince someone to accept Q on the basis of a modus ponens argument, he must get them

to accept the validity of modus ponens as a principle, which amounts to having the tortoise

1

accept an additional true premise along with P and P → Q: (P ∧ (P → Q)) → Q.1 One

might see this as superfluous, but nonetheless, with this premise in hand surely someone

must be convinced of Q. Unfortunately, it is recognized that such an argumentative move

is inadequate for the hardened skeptic, who will note that acceptance of Q in this case

depends still on an application of modus ponens (and, we might notice, and-introduction).

Achilles might be tempted to try a similar manouvre again, getting the skeptic to assent

to another true principle, which he readily will do: [P ∧ (P → Q) ∧ (P ∧ (P → Q))]→ Q.

But of course, this forces an acceptance of Q, once again, only if one accepts an application

of modus ponens. We are obviously on road to an infinite regress.

Russell succinctly describes the problem by saying that logic is lacking “the notion of

therefore, which is quite different from the notion of implies, and holds between different

entities... In the first of these [notions], a proposition is actually asserted, whereas in the

second it is merely considered.”2 The idea here is that the two premises, P and P → Q,

function differently such that the ‘P,’ supposedly common between them, is to be read as

two different sorts of things. Much more, of course, can be said about Russell’s view, but

what can be taken away here is that any response to a skeptic of Carroll’s kind must make

use of some notion beyond truth—be it a more nuanced way of individuating propositions,

or a further concept of “therefore.” Some notion along these lines will surface at the end

of chapter two, and then again in chapter four.

We will see the challenge of Carroll’s skeptic throughout all of the thesis, but there

is one further thing to note now: what if Tortoise did not accept (P ∧ (P → Q)) → Q?

The story goes that Tortoise doubts this hypothetical, but the next assertion of modus

ponens quells this doubt. It is only when moving from this additional hypothetical to the

conclusion, Q, that the skepticism properly returns, and then repeats. In other words,

Tortoise assents to the use of modus ponens, but not to the epistemological “force” of

logic. One can easily see then where a far more disastrous doubt so enters: deny the

hypothetical outright. This amounts to a skepticism about modus ponens, or about, more

generally, certain logical rules. One might, for example, infer by a different set of logical

rules than someone else, and if this were case, it would seem that some way of settling the

1Carroll (1995)2Russell (2009)

2

matter is needed. Call Carroll’s story, where the skeptic is interested in force, a type-2

skepticism; and this other more sweeping concern about ‘which rules are the right rules,’

type-1 skepticism.

In the case of Tonk, or more generally ‘bad connectives,’ it will be best to follow Prior’s

original construction of the issue. Say we want to know what the conjunction connective,

and, ‘means.’ Then given a set of introduction and elimination rules which show us the

formal application of the connective, we know the meaning “for there is simply nothing

more to knowing the meaning of ‘and’ than being able to perform these inferences.”3

Consequently, ‘and’ means just what is specified by:

1. From any pair of statements P and Q we can infer the statement formed by joining

P to Q by ‘and’

2. From any conjunctive statement P-and-Q we can infer P

3. From any conjunctive statement P-and-Q we can infer Q

or, more formally:

‘And’ Introduction:P QP ∧Q

... and ‘And’ Elimination:P ∧QP

P ∧QQ

Insofar as one was willing to go along with this understanding of meaning, everything

appears to be in place: ‘And,’ the logical connective, means just what it does by the

way it figures in our logical reasoning—that when we know (or accept) two propositions

then we can inferentially combine them to form some conjunction, and that we can infer

each conjunct when we know (or accept) the whole. Now, we might ask, ‘what was this

connective “Tonk,” and if its meaning can be understood so, then what are its rules of

use?’ So,...

‘Tonk’ Introduction: PP -tonk-Q

... and ‘Tonk’ Elimination:P -tonk-Q

Q

With just these rules one should now be able to provide a semantic reading of the

connective: ‘Tonk’ means just what it does by the way it figures in our logical reason-

ing—that when we know (or accept) some proposition we can inferentially combine it with

3Prior (1960)

3

another to form some ‘Tonk’-conjunctive (or “contonktive,” if one prefers), and that we

can always infer it’s latter proposition (in this case, Q). These rules, one might notice,

also match the disjunction introduction and conjunction elimination rules—rules we take

to be meaningful and largely unproblematic—and so, if there is a problem, then it will

not be with the rules individually. At this point, however, the problem does become quite

clear: if we infer according to Tonk, then anytime we believe anything, or take anything

to be a premise, then we can conclude anything. As noted previously, if one finds this

view of meaning regarding connectives plausible, then they must also adopt some further

meta-logical principle to guide their selection of the rules, or, otherwise, must find good

company with Tonk.

Considering the broad applications that these three issues raise, it would seem as

though all must be addressed if one hopes to present a foundation for logic, its use and

truths. Thus, I begin in chapter one by exploring a prominent account which attempts

just that.

Paul Boghossian, in his paper “Knowledge of Logic,” considers a range of views on

logical foundations—particularly, non-factualism, default-reasonable beliefs, and conven-

tionalism—but finds that each position suffers in some manner, and so in spite of its own

problems, concludes that we are forced to accept some version of conceptual role semantics

as the best option among a problematic bunch. Conceptual role semantics provides us

with a way of understanding connectives such that Tonk would properly be ruled out, but

it brings with it some important consequences which I will try to show might leave one

with a lingering ‘bad taste:’ the rejection of an epistemic principle, “the principle of the

universal accessibility of reasons,” and the startling conclusion that the type-1 skeptic can

not be answered. Subsequently, I will take it that the book must be re-opened on the

outstanding issues of other positions.

To that end, in Chapter 2 we will explore Bob Hale’s position, presented in his paper

“Basic Logical Knowledge,” as our exemplar of accounts that take our basic logical beliefs

to be “default reasonable.” I will attempt to show that this account, and a handful of

relevantly similar ones, must contend with a number of strong criticisms, some possibly

irredeemable. Of particular note is the problem of epistemic access: in attempt to answer

Carroll’s Tortoise, Hale finds that one must accept “a species of non-inferential intellectual

4

recognition—which we may as well call rational insight”4 to ‘ground’ a logical argument.

What is the nature of this insight? What is it about entailment that we ‘recognize’?

From discussion of these issues, I attempt to draw out a number of conclusions (most

explicitly in section 2.4) which will motivate an entirely different approach; and so, Chapter

3 will discuss Hartry Field’s ‘non-factualist’ position which both involves a different route

to justification as well as a different grounding for logical semantics. I will try to show that

what non-factualism appears to strike upon correctly is emphasizing the methodological

application of logic to the world; but also, that Field’s position falls prey to an issue not

unlike that which Boghossian’s position faces.

Finally, I question in chapter four what amendments may be made, if any, to bolster

non-factualism. I will propose a distinction for Field’s notion of an evidential system which

will clarify both the non-factualist position itself as well as how one might go about address-

ing this thesis’ overarching problems. Here we will see a variety of points from throughout

the thesis raised, and particularly Russell’s distinction, once again, about assertion and

reference.

4Hale (2002), pg. 298

5

Chapter 1

Rule-Circularity and Conceptual Role Semantics

The first section of this chapter introduces Boghossian’s conceptual role semantics and

two constraining principles which specify the relationship between conceptual roles and

our justification of our beliefs. In the following sections I show how Boghossian’s position

addresses our three main concerns, and especially, in section 1.3, I show the usefulness of

rule-circular argumentation. There is, however, one preliminary remark to make regarding

the relationship between rule-circular arguments and Boghossian’s argumentative path to

conceptual role semantics.

Boghossian finds that he is led to his position, not simply by its own merits, but rather

by the lack of any compelling alternative. Among his critical discussion of competing

views, he resuscitates the criticism of rule-circular argumentation—originally lodged at

Boghossian himself by Gilbert Harman—that “one’s warrant for a principle of logic cannot

consist in reasoning that employs that very principle.”1 Particularly, Boghossian finds that

empirical approaches to logic fundamentally depend on this sort of argumentation and so

claims that such approaches are ‘no real alternative’ so long as one cannot use rule-circular

justification.2

Subsequently, after all other options have been exhausted and Boghossian returns to

what he calls ‘the inferential’ approach, which does use rule-circular reasoning, he gives up

some of what makes conceptual role semantics more compelling than the empirical picture

1Boghossian (2000), pg. 232.The original context comes from Boghossian (1996) and Harman (1996)2See: Boghossian (2000), pg. 232-234 (“An Empirical Justification For Logic”)

6

(precisely the ‘you too’ criticism that the logical empiricist needs rule-circular reasoning).

Just as he notes the fact that bans on philosophical and argumentative tools ‘go both

ways,’ it would seem that, at least to the limit of inconsistency, so does permission.3

Consequently, I propose (and will attempt to show in section 1.3) that the sort of rule-

circularity he defends can be seen as amenable to a variety of other positions; and this

is of particular importance because plausible strategies which deny any circularity at all

(rule-circular or otherwise) are limited in number. With that said, we may now turn our

attention to conceptual role semantics and Boghossian’s position on the justification of

logic.

3Boghossian’s particular remark on the matter...

“For if we are barred from supposing that reasoning using a given logical principle can recon-struct an a priori warrant for that very principle, are we not equally barred from supposingthat it could reconstruct an empirical warrant for that principle?” (Boghossian (2000)), pg.233)”

7

1.1 Meaning As (Almost) Use

Conceptual role semantics is broadly the view that the meaning of some thing is given by

the ‘conceptual role’ it plays. This notion can be very expressively powerful—the meaning

of anything (action, proposition, word, thought occurrence, etc.) is to be given by the

conceptual role it plays for a perceiver of that thing—or quite limited in its scope—there

is a subset of phenomena which is best or partly explained (leaving open other meaning-

avenues) by the conceptual role it plays for one of either an agent perceiving or acting.

The historical details surrounding the origin of this theory are hazy, but it can at least be

attributed to the family of views regarding “meaning as use.”

This should feel in some sense familiar, as it is not too far off from the idea that

introduction and elimination rules provide meaning for connectives by specifying how we

can begin and end our inferences with them. ‘And’ means just the inferences possible, given

a set of statements, that form their conjunctions; and just the inferences possible, given a

set of conjunctions, that dissolve them into their respective conjuncts. It is not immediate

that any ‘intro/elim’ semantics will turn out to be of the conceptual role variety,4 but if one

begins with the idea that meaning tracks differences (or, possible differences) in thought,

then it is certainly clear that there must be a ‘role reading’ of introduction and elimination

rules so long as they properly individuate connectives. Otherwise, one becomes committed

to the idea that there are things that are properly differentiable from one another on the

basis of their conceptual role but that do not incur different thoughts in the differentiator.

In other words, one would be committed to the idea that ‘and’ and ‘or,’ are different

logical connectives to the extent that their introduction and elimination rules determine

what different inferences are possible, but that we should expect no difference in the actual

inferences, the thoughts or behaviour, of someone using ‘and’ and some other using ‘or.’

Of course, it is possible to conceive of such cases where one’s reasoning from some premise

to some conclusion might be aptly described by a variety of rules, but the contention here

is systematic.5

4For example, one may be more inclined to read such schematic rules as an instance of structuralsemantics. See Peregrin (2008) or Peregrin (2017) for more details.

5And outside of just the logical realm, one might consider the case of frogs snapping at ambient blackdots, confusing them for flies. The conceptual role of flies is such that the frogs snap, expecting food;

8

Boghossian makes his variation of the theory clear by noting that:

“Of all the inferences that ‘if, then’ can and does participate in, a specific

subset is responsible for fixing its meaning. Given that subset, ‘if, then’ means

that unique logical concept, if any, whose semantic value makes the inferences

in that subset truth-preserving.”6

There are two functioning parts to this: first, that the logical concept has a semantic

value, responsible for determining whether or not the rule is truth-preserving, apart from

the rule’s use by a person; and second, inferences which are not truth preserving do not

have their meaning fixed. There is also the important qualification, “if any,” which tells

us that we may infer by a rule (whether it’s called ‘if, then’ or ‘Tonk’) which does not have

any conceptual role at all. In other words, conceptual roles do not determine our actual

inferential behaviour, only the meaning of some of our behaviour.

These moves, however, afford Boghossian the opportunity to cash out entitlement in

a non-conventionalist manner. Through the principle, (L)—“if M is a genuinely meaning-

constituting rule for S, then S is entitled to infer according to M, independently of having

supplied an explicit justification for M”7—we can say that one is entitled to their inferences

in just those cases where their behaviour ‘lines-up’ with the logical concepts, the meaning-

ful conceptual roles. It should be noted that (L) is stated in a relative manner: “if M is a

genuinely meaning-constituting rule for S, then...”; despite the seemingly universal condi-

tion for meaning, the existence of a concept which makes an inference use truth-preserving,

Boghossian states the idea in this weaker form. Momentarily, we will see how ‘universality’

comes to play a part in Boghossian’s position and in addressing our main concerns.

As a final piece to the puzzle, we must find some way of moving from generally

being entitled to our inferences, to being justified in our particular inferences. For this,

and the conceptual role of the ambient dots is not sufficiently different, the phenomena is not sufficientlydifferentiable, prompting the same behaviour—as if the flies and dots were the same thing. Of course,flies and ambient black dots are far from the same sort of thing, but a conceptual role semantics wouldimply this is precisely because the phenomena have different conceptual roles for us, which both entailsour behavioural differences to flies and dots, and our different thoughts and reasoning about flies and dots.Dretske (1988) provides good commentary for further interest.

6Boghossian (2000), pg.248-2497Boghossian (2000), pg.249

9

we require something more powerful than just (L), and this is where Boghossian believes

rule-circular argumentation will come into focus. Though I leave the full explanation of

this aspect to section 1.3, it can be said now that there is a distinction between grossly

circular arguments and rule-circular arguments; particularly, that rule-circular arguments

do not ‘assume’ the rule as a premise, but instead apply it in the argument. Consequently,

Boghossian concludes by another principle, (RC)—“S’s rule-circular argument for a rule of

inference M will confer warrant on S’s belief that M is truth-preserving, provided that M

is a genuinely-meaning constituting rule for S”8—that so long as there is a conceptual role

for the inference in question (that the inference is a meaningful one), then a rule-circular

argument will succeed in taking one from a naive belief about the rule to a warranted one.

In sum, Boghossian’s conceptual role semantics seems to give us a substantial reading

for the meaning of logical connectives and a way of comparing or explaining our behaviour

in relation to logical connectives: conceptual roles exist as behaviour-independent concepts

which have a “semantic value” that differentiates our implicated inferences from other in-

ferences. Particularly, it is the property of truth-preservation that separates the meaningful

connectives and inferences from those which are not; and when dicussing these meaningful

rules, we can construct a justification through rule-circular means. Now, we can explicitly

turn our attention to the capability of conceptual role semantics to deal with Tonk and

our skeptics.

8Boghossian (2000), pg. 250

10

1.2 Solutions: Better and Worse

Let’s begin with the problem of ‘bad connectives.’ Tonk appears to be a well-defined

connective (from the perspective of introduction and elimination rules), just as any other

logical connective is (say, the otherwise uncontroversially accepted ‘And’), and yet Tonk

trivializes our language. Any system containing Tonk will license one to infer anything

from anything else. Consequently, its hard to see what Tonk could have ever meant in the

first place, and why we might be justified in using other logical connectives specified in the

same manner. So, how might Boghossian’s position help with warding away connectives

like Tonk without throwing away ‘And’ or ‘If, Then’? So long as we understand ‘genuinely

meaning constituting’ to entail “truth-preserving,” then by the principle (L), one is never

entitled to infer according to Tonk.

So far, so good; but, one may press, this presents a new dilemma: either (A) this

does not stop one from ever having the conceptual role, or the logical idea, specified by

Tonk, only their entitlement to their infence is in question; or (B) it shows that we can

infer—though not entitled to do so—according to Tonk, without there being a conceptual

role at all. In the first case, it seems troubling that we might have conceptual roles

which we are not entitled to. In other words, there is a dependency between our actual

behaviour and the existence of conceptual roles which would rule out large swaths of what

we do (say, any accidental misapplication of ‘if, then’) as meaningless. And in the second

case, it seems troubling because the connection between our behaviour and the meaning-

constituting features of our behaviour (properties of truth-preservation, say) are eroded.

In other words, we can infer, and distinguish or describe our own and other’s inferences,

without reference to an ‘actual’ conceptual role. What then is needed is an account of how

conceptual roles arise at all and, subsequently, what is different about the truth-preserving

connectives that is more than mere convention.

It is not completely clear what sort of metaphysical view would ground this distinction

between meaning-constituting and non-meaning constituting inference rules. On one hand,

an avenue available to Boghossian is a view that we might describe as metaphysically

loaded, in which some connectives somehow exist in the world—i.e. that there are patterns

of inference, some of which have a property of truth-preservation, and meaning-constitution

11

derives from a particular pattern having a particular property. In this case, there are facts

and truths about logic, and the genuinely meaning constituting connectives are genuinely

about the world, and (presuming classical logic is correct) the logic we teach with truth

tables is a description of these facts. In a sense, this is captured by Boghossian’s own

comments when he remarks that “there is no proposition expressed by sentences of the

form ‘A tonk B.’”9 In what way would the world have to be such that ‘A tonk B’ was the

unique logical idea needed to describe it? However, it is not clear that this is either the

view that Boghossian is advancing, nor itself a plausible one. For starters, what sort of

experience would one need to have to recognize that ‘And’ was an appropriate description

of the world; and furthermore, how, by what faculty, would such a recognition be made?

On the other hand, and in attempt to avoid such metaphysical qualms, an avenue may

seem available along conventionalist lines alone. So, instead of appealing to the truth-table

‘out there,’ it could be said that this is merely a well-functioning descriptive tool. I will

not attempt to take up such debates here, only note that this does not help conceptual

role semantics; for if it is conventional (by choice) that we appeal to truth-preservation for

meaning, then it is at least possible that a different question (say, of monotonicity instead

of truth-preservation) could be used to determine which connectives are “genuine” and

which are meaning-vacuous.

There is, however, another issue lurking in this discussion of truth as well; namely, the

idea that Tonk does not preserve truth. Recognizing the fact that each half of the Tonk rules

is itself a well-established and truth-preserving rule—where tonk-introduction is identical

to disjunction introduction, and tonk-elimination identical to and-elimination—conflicts

with, as Hale describes, “the well-entrenched, and surely correct, thought that we can’t

pass from true premises to a false conclusion by chaining together steps of reasoning each

of which is truth-preserving.”10 At which particular step in the process does truth fail

to be preserved? Subsequently, it is difficult to see how, conceptual role or not, taking

‘genuinely meaningful’ to entail ‘truth-preserving’ will get one very far to begin with. Are

conceptual roles entities which specify individual rules and so Hale is wrong about about

the “well-entrenched” idea about truth-preservation, or are conceptual roles entities which

9Boghossian (2000), pg. 25110Hale (2002), pg. 293

12

mark out tuples of rules?

That all said, Boghossian admits that his presentation of the position is partly an

“IOU”, to be explained in full in the future, and rightly recognizes the force of many

criticisms. If such a story is to be presented, then perhaps conceptual role semantics is

plausibly positioned to deal with Tonk. What then of the logical skeptics?

Regarding our type-1 skeptics, the IOU still looms large. Recall that this sort of

skeptic questions logical rules to begin with; so, without a story about where conceptual

roles come from and why truth-preservation is the correct question to determine meaning,

the conversation on this front is doomed to fail. If one begins with the idea that ‘if,

then’ is meaningful because it is truth-preserving and that this is a matter of convention,

then the skeptic can merely deny that the rule is meaning-constituing on the grounds of

different conventions. Insofar as conceptual roles are to be identified in opaque non-public

terms (say, ‘the language of thought’)11 one lacks any evidence to show the skeptic for

exactly what reason some logical rule is meaning constituting. If we add in an explanatory

story—say, of the metaphysically rich truth sort—then one is afforded some external basis

to which they may appeal for warrant; but this would also require the caveat that whatever

so figures one person’s conceptual roles is, at least, capable of determining another person’s

conceptual roles. Otherwise, even with this explanatory story, one must contend with two

issues: (1) the skeptic could deny that the formation of your conceptual role was necessary

(that whatever the contingent facts are that arise in one’s belief of, say, ‘And’, leads them

instead to a belief in ‘Tonk’); and (2), if one is capable of forming a conceptual role that

another is not, then what’s to say that one’s belief in ‘Tonk’ is not warranted by their

conceptual roles, roles another person simply has not or could not form?

Boghossian notes this exact line of argument and finds it problematic; not, however,

because of the reasoning. Rather, what Boghossian concludes is that to entertain such

skepticism at the outset is seriously misguided. Instead, one should recognize an underlying

11Boghossian seems to encourage this idea when he says that, regarding the plausbility of (L): “if it istrue that certain of our inferential dispositions fix what we mean by our logical words (in the languageof thought), then it is very plausible that we should be entitled to act on those inferential dispositionsprior to, and independently of, having supplied an explicit justification for the general claim that theyare truth-preserving.” (Boghossian (2000), pg. 250, emphasis mine) That Boghossian is interested in thelanguage of thought presents an interesting and possible path forward for conceptual role semantics, butany such discussion would involve a much broader historical discussion of the philosophy of mind.

13

and pernicious assumption in epistemology broadly:

The Principle of the Universal Accessibility of Reasons (UAR): “If something

is a genuine reason for believing that p, then,... its rationalizing force ought to

be accessible from any epistemic standpoint.”12

If one holds strong to this idea, that what is a reason for me must be a reason for you,

then they will find the type-1 skeptic compelling; and so, to avoid the argumentative doubt

about which meaning-constitutive logical property is the ‘right’ one, will need an answer

to the conceptual-role IOU. However, Boghossian denies (UAR) and instead advocates for

the idea that there may not be such universal reasons for logic.13 Consequently, there is

both admittance and acceptance that the type-1 skeptic cannot be answered. Whether or

not it makes sense to deny (UAR) is food for thought, but at first glance it should seem

worrisome. If eschewing this principle stops ‘reason-monsters’ from setting the evidential

agenda for everyone else, then maybe it’s not such a bad thing; but if rejecting (UAR) also

stops significant conversations about evidential common ground from taking place, then

perhaps the trade-off is not worth it. What then, of the type-2 skeptic? If someone accepts

the use of a logical rule, but does not assent to or accept it’s conclusions in practice, can

conceptual role semantics say anything about the matter? This involves a much closer look

at rule-circularity and how we might move from ‘mere entitlement’ to actual justification.

12Boghossian (2000), pg. 25313To be clear, Boghossian does not take this to be a full epistemological position for everything; only

for those skeptical questions, like the existence of the external world, which create sharp and seeminglyunanswerable lines in inquiry.

14

1.3 The Role of Rule-Circularity

Boghossian proposes that there are five plausible categories for answering whether or not

logic can be justified (or more particularly, basic logical rules like modus ponens): total

skepticism (no justification), non-factualism about logic (no justification), non-factualism

about justification, default-reasonable beliefs, and rule-circular arguments;14 and consider-

ing the failures of the first four, one must look for a method of rule-circular justification.

Though Boghossian’s particular concern is not as broad as ours, we will see that his con-

struction of rule-circularity is a step-forward to answering the type-2 skeptics; particularly

because the warrant afforded by a rule-circular argument directly addresses the infinite

regress of hypotheses. In section 1.1 we briefly glossed what function rule-circular argu-

mentation served in Boghossian’s overall picture, but now we will need to see exactly what

counts as a rule-circular argument, why it may be permissible, and what consequences one

has.

Crucially, a rule-circular argument is one which relies on the rule ‘in question,’ but

which does not ‘beg the question.’ So, a rule-circular argument is one which establishes

the conclusion of an inference rule, on the basis of that rule, but not with that rule as an

assumed premise. For example, Crispin Wright’s rule-circular argument for Tonk:

1. ‘P tonk Q’ is true iff ‘P’ is true tonk ‘Q’ is true Meaning Postulate

2. P Assumption

3. ‘P’ is true 2, T-Scheme

4. ‘P’ is true tonk ‘Q’ is true 2, tonk-introduction

5. ‘P tonk Q’ is true 4, 1, biconditional-elimination

6. P tonk Q 5, T-Scheme

7. If P, then P tonk Q 6, logic

14See Figure 10.2 and pages 235-236 in: Boghossian (2000)

15

Here, the use of tonk-introduction is never explicitly assumed anywhere in the argument

(at least, and importantly, not as a premise); instead, what is being established is that

“this template is available to explain how someone for whom inference in accordance with

tonk-introduction was already part of their unreflective practice could arrive at an explicit

justification for it.”15 And so, a rule-circular argument is really a general strategy for ex-

plaining how an inference rule works, and implicitly why (because of it’s truth-preservation)

it will continue to work: “what we have is an argument that is circular only in the sense

that, in purporting to prove the validity of a given logical law, it must take at least one

step in accordance with that law.”16 The broad idea here is that a rule-circular argument

is an explanation of a rule, it makes explicit the function of a rule, but is not a persuasive

argument because it relies on the prior acceptance of the rule.17

It is worth immediately pointing out that while Boghossian acknowledges that rule-

circular arguments can be posed for any connective, and as we just saw, Tonk included,

he does not want to allow complete freedom in their use; and so, he provides much needed

buffer in the construction of his principle (RC):

“(RC) S’s rule-circular argument for a rule of inference M will confer warrant on

S’s belief that M is truth-preserving, provided that M is a genuinely meaning-

constituting rule for S.”18

Now, it would seem, that we can answer the type-2 skeptic without giving up ground to all

connectives. A rule-circular argument provides justification for our conclusions by a rule of

inference so long as that inferential pattern is “genuinely meaning constituting.” If Tortoise

were to ask for a further hypothetical, the rule-circular-arguer could refuse to entertain the

regress on the grounds of the rule’s validity being proven; Achilles could respond by saying

‘look you have accepted that modus ponens is a valid inference, and so you can entertain

as many hypotheticals as you want but it will not matter—“one step” in accordance with

the rule is all that was needed to show this conclusion must be right.’ This will be an

important tool to keep in our pocket going forward, but note that in it’s current form, the

15Boghossian (2000), pg. 24716Boghossian (2000), pg. 24517This distinction originally shows up in Dummett’s work as the difference between ‘pragmatic’ and

‘vicious’ circularity. See: Dummett (1991), especially Chapter 9.18Boghossian (2000), pg. 250

16

success of rule-circular arguments depends upon the same problematic story from earlier:

how exactly do we know when a rule is genuinely meaning-constituting? The visage of our

‘IOU’ comes into focus once again.

When discussing the source of entitlement, Boghossian rightly confronts this exact line

of questioning:

“What makes a rule meaning-constituting? This is one of the questions that

still awaits a definitive answer. My present concern, however, is just to em-

phasize that our problem about our entitlement to employ a rule of inference

reduces to that problem, a problem that any conceptual-role semantics faces.”19

And so what we can take away from this, is that (RC) is not a strategy solely related

to conceptual role semantics. The principle (L) tells us that we are entitled to infer by

genuinely meaning-constituting rules even if we have not gone on to show their validity

or provide some other justification—that is, (L) tells us which rules we should want to

construct rule-circular arguments for. Unless it can be shown that the only way to make

a rule meaning-constituting is through the conceptual role that has some ‘semantic value,’

then it would seem that both (L) and (RC) are really general strategic moves available to

a variety of positions. The questions that follow, among others, are which positions, how,

and why? However, it is far from the present concern to attempt to answer this in detail.

What should be noted is that unless another epistemological position contains some other

principle, call it (NoRC), which states ‘if M is an inferential rule for S, meaning constituting

or not, then S is entitled to infer according to M, only when an independent and explicit

justification for M has been provided,’ then the rule-circular approach is ‘allowed.’ This is

of importance, if only, because the explanation which rule-circular arguments afford make

quick work of the type-2 skeptic and it is in our interest, then, to find other positions

compatible with rule-circular argumentation.20

To conclude, Boghossian provided us with an argumentative strategy for dealing with

Carroll’s Tortoise, but failed to provide a compelling account of what it meant for some

19Boghossian (2000), pg. 25020Authors may rightly express doubts or concerns about the use of rule-circular argumentation, but

these hesitations should not be confused with genuine incompatability. Avoiding the use of a tool is, ofcourse, quite different from being unable to use some tool.

17

logical rule to be “meaning-constituting.” Subsequently, the attempt to rule out Tonk was

undermined and the type-1 skeptic unanswered. These further issues followed entirely from

postulating a conceptual role which fixed the meaning of connectives, and it was shown

that neither (L) or (RC) were implicated in the problems. Now, the following two chapters

will explore a couple of alternative epistemic ideas which capture two broader strands of

approaches to the justification of logic. The first will primarily focus on Bob Hale’s idea

of the ‘minimal inference kit,’ and the latter, Hartry Field’s non-factualism about logic.

I will attempt to show what these positions are and how they differ; what the problems

with the views are; and whether or not they are amenable to rule-circular argumentation,

so that we may come to find an adequate answer to all three of our problems.

18

Chapter 2

Logic with an Epistemological Foundation

Five key claims differentiate Hale’s justification of logic:

1. That logical knowledge is “a priori knowledge of a conceptual necessity.”1

2. That we must accept a principle which underpins what it means to understand some-

thing; namely, that acceptance of logical concepts is necessary for understanding

them.2

3. That the minimum standard of acceptability for a logical rule is that it be sound,

that it will never lead from true premises to a false conclusion.

4. That we must accept a principle which explains our entitlement; namely, that one is

entitled to a logical belief when that belief is “immune to rational doubt.”3

U. That rule-circular arguments are not capable of justifying one’s use of a logical rule.

The first item can be better explained by saying that there are facts about our logical

connectives, like their being able to preserve truth or not, which we come to know apart

1Hale (2002), pg. 2832We focus on logical concepts here for two reasons: first, both Hale and this thesis are primarily

concerned with logic; and secondly (and more importantly), it is not clear that Hale believes that thisprinciple will apply to all concepts or only those concepts outlined by the first item. There is a muchbroader reading of “acceptance as understanding” which would implicate discussion of ‘slabs’ and ‘chairs’and take us full course into “meaning as use” but this is not clearly what Hale has in mind. Later, I willdrop specific reference to logical concepts, but this a matter of convenience—one may continue to readthis principle as always and only referring to logical concepts.

3Hale (2002), pg. 304

19

from any sort of empirical discovery. These facts are significant because, in modal terms,

they stand in a necessity relationship to all possible sets of principles (or, axioms, if one

prefers) and their negation stands in no possibility relationship to any possible sets of

principles.4 In other words, these facts about the connectives, like their truth-preservation,

are True—they are unchanging, immutable, indefeasible, could not be any other way—and

any doubt about these facts, as a priori concepts, while possible to be raised, could never

be substantiated. This is not just to say that ‘facts of the matter’ lead us to say these

concepts are true, but that it is by the nature of the concept itself that it is true.

The principle of the second claim, that acceptance is necessary for understanding, tells

us that if one properly understood some concept, then they would behave in accordance

with it. In the realm of logic, what Hale is after is a reading of logical connectives such

that if one can be said to properly understand what “if, then” means, for example, then

they would not deny the conclusion in a modus ponens argument—they would behave in

accordance with it. As foreshadowing, then, “acceptance as understanding” is a principle

aimed to discount the type-2 skeptic: how could one claim to know what the conditional

means and, when presented with a well-formed modus ponens argument, refuse to assent to

its conclusion? We will also see that this principle directly addresses, more generally, those

who would doubt the sorts of conceptual necessities Hale takes basic logical knowledge to

be.

The third item tells us by what means we will differentiate “genuinely meaning-

constituting” rules from ‘meaning-vacuous’ rules (to use Boghossian’s distinction). Hale

argues that a truth-preservation criterion will not adequately bar us from using connectives

like Tonk (for the Tonk rules are comprised of two otherwise accepted and truth-preserving

rules), but that when we turn our attention to soundness, we will be left with a much more

restricted set of connectives. More particularly, the soundness of many rules can be proved

from the assumption of a much smaller set of rules, a ‘minimal kit’—the rules for the

4This technical definition is intended to capture Hale’s discussion of those concepts which may berelatively necessary compared to absolutely necessary; and the use of ‘principles’ is intended to capturethe notion of “laws” which make sets of premises. For example, it may be that some proposition p mustbe true, but this is because of ‘the laws of physics;’ and so taking the laws of physics to be representedby φ we would say that p is “φ-ly necessary”. See: Hale (2002), pg. 280-283 for further detail. However,the reader may gloss this understanding of absolutely necessary in favour of “could not be any other way”and do just as well.

20

conditional operator and universal quantification. Of course, one may note that this leaves

modus ponens and quantification as assumed, but this is where item four comes into play.

One is entitled to an inference patterm if that pattern is immune to doubt. The picture to

come will try to show that the minimal kit of rules satisfies the sort of conceptual properties

of item one, and that then concepts of the sort item one specifies satisfy the conditions of

item 4.

Finally, ‘item U’ tells us that rule-circularity is a seemingly unsatisfactory approach

to justification. I mark this claim separately because while Hale advocates for avoiding

rule-circular argumentation, it is not clear that he could not employ some principle like

Boghossian’s (RC). Particularly, Hale presents three complaints that one must wrestle

with. First, it is not clear that the rule is not being ‘assumed’ and so that it is not vicious

circularity when we focus on soundness. Here, the worry is that proofs of soundness, say for

modus ponens, depend upon the soundness of modus ponens; and so, an assent to the rule

as sound is already being taken for granted.5 Second, it is not clear that rule-circularity

is not viciously circular when we focus on knowledge, when we focus on how we come to

know rules. Here, the worry is that the explanatory aspect of rule-circularity does not

provide us with any epistemological footing for our use of the rule, it merely explains our

coming to a conclusion. And third, it is not clear how we might constrain rule-circular

argumentation. Here, the worry is that we will allow a justification of bad connectives if

we do not have some further specification (and what could that specification possibly be?)

for rule-circularity.6

It is important to recognize that these criticisms are not new to our discussion of

rule-circularity. In the case of soundness what we really have is a special case of the

circularity generally—all rule circular arguments require at least one step with the rule.

That we should be careful about soundness is a product of Hale’s position on soundness

proofs being the correct tool for justifying rules and his own concern that this will involve

circularity. When focusing on the circularity in ‘knowledge,’ we are really calling into

question the explanatory vs. persusive distinction to begin with—the difference between

a rule-circular argument explaining away our regress of hypotheticals, and a rule-circular

5Note, one might reasonably read this as Hale invoking the type-1 skeptic. Boghossian asked for only“one step” in accordance with the rule, but this, to Hale, is already begging the question.

6See: Hale (2002), pg. 285-288

21

argument convincing a type-1 skeptic. Yet, a rule-circular argument can be restricted to

the narrow use of explanation and justificaton. And finally, Hale’s concern for constraining

rule-circular arguments we have seen come up explicitly in the construction of Boghossian’s

(RC) already. This criticism would only apply in cases where one did not include the

“genuinely meaning-constituting” aspect.

In summary, Hale’s position goes something like this...

One is entitled to their logical belief when it is immune to doubt. This will

mean that one is only entitled to those beliefs which are a conceptual neces-

sity—a priori and inconceivably, impossibly false. Those logical beliefs which

are conceptual necessities are the one’s which must be assumed to put forward

proofs or make arguments about other logical beliefs. In other words, one will

always be entitled without qualification to modus ponens and universal quan-

tification introduction, because these are the only rules which cannot be proved

without assumption.7 And if someone were to attempt to doubt such a logical

belief, they will really have shown themselves to misunderstand the belief; for

if they grasped the meaning of the belief, then they would have acted in accor-

dance with it. Finally, no route seems available by rule-circular argumentation.

Now, then, we may turn our attention to how this position deals with our guiding issues.

7Admittedly, Hale also seems to think that the strategy of a reductio should be included in this set,but recognizing the discussion of negation to be out of scope, sticks only with quantification and theconditional.

22

2.1 Problems (Two Different Ones)

In similar fashion to the first chapter, let’s begin with Tonk. How does Hale’s view ward

off problematic connectives? There is a trivial sense in which Tonk fails to be discounted by

our gloss of Hale: of course it could be used to prove things about other logical beliefs—one

literally can make a tonk-argument—but this would not put Tonk on the same playing field

as other connectives, like the conditional, for two reasons: (1) it is not clear that Tonk is

a conceptual necessity; and (2) it is not clear that, if we restrict our interest to proofs of

soundness, that Tonk is a practical necessity. What I mean to point out here is Hale’s idea

that whatever connectives we are going to accept without a supporting explicit argument

should be “indispensable.”8 To see how this works, we can examine Hale’s argument for

the unsoundness of Tonk:

1. Tonk-intro allows you to make any inference of the form ‘A, so A tonk B’

2. If the inference: ‘p, so p tonk q’ is of the form ‘A, so A tonk B’, then tonk-intro

allows you to make it

3. The inference: ‘p, so p tonk q’ is of the form ‘A, so A tonk B’

4. Tonk-intro allows you to infer ‘p tonk q’ from ‘p’

5. Tonk-elim allows you to make any inference of the form ‘A tonk B, so B’

6. If the inference: ‘p tonk q, so q’ is of the form ‘A tonk B, so B’, then tonk-elim allows

you to make it

7. The inference: ‘p tonk q, so q’ is of the form ‘A tonk B, so B’

8. Tonk-elim allows you to infer ‘q‘ from ‘p tonk q’

9. Tonk-intro and tonk-elim allow you to infer ‘q’ from ‘p’

10. The tonk rules together allow you to derive any conclusion from any premise

8Hale (2002), pg. 299

23

11. Hence, Tonk is not sound

Lines [1.] and [5.] are meaning postulates for the rules of Tonk, and every other line

is either an instance of universal instantiation or one of the conditional’s rules. Hale’s

idea in working through this proof is to show that “any vindication of a doubt about the

conservativeness (or, more generally, the soundness) of any rules of inference must involve

reasoning which doesn’t use those rules, but uses some other rules instead—rules whose

reliability is assumed in that reasoning;”9 and while it is not immediately obvious that

modus ponens will always be the rules needed to prove soundness for any other rule, Hale

contends that “any rule(s) of inference whose soundness we may wish to consider will—or

so I think we may assume—be both general and conditional—general, in the sense that

their explicit forumulation tells us that a conclusion of some specified general form may

be drawn from premises of some specified general form, and conditional, in the sense that

they tell us that given premises of the specified form, a conclusion of the specified form

may be drawn.”10

The result is a “minimal kit” of inferences comprising of the conditional and universal

quantification, which must be, in some sense, taken for granted, since any attempt to prove

their soundness will be circular (since all proofs of soundness are conditional and general);

and note, this kit does not include Tonk, for there is little sense in which Tonk will be

“indispensable” to proving soundness. So far, so good; though it would seem that both

skeptics have a fair bit to say on the matter. Beginning with the type-2 skeptic, what

might Hale then say to one who accepts some rule, say the whole ‘minimal kit,’ but refuses

to assent to the conclusion of one of its applications?

Regarding this issue, the principle of “acceptance as understanding” makes quick work

of Carroll’s Tortoise: any skeptic simply does not understand the rule they are doubting.

It is a necessary condition of their properly understanding the rule that they accepted it,

and they doubted it; so, they did not accept it; so, they did not understand it; so, it would

seem, their doubt should not be taken seriously. On this principle, Tortoise should consider

giving up Euclid for football. Before declaring the matter dealt with, however, exactly how

this principle is functioning will be worth a moment of close inspection. Particularly, there

9Hale (2002), pg. 296-29710Hale (2002), pg. 299

24

appear to be two issues: how do we square acceptance as understanding with Hale’s position

against Tonk; and, how do we deal with the anomolous cases of competent dissidents?

For the first issue, we can break down acceptance as understanding into two separate

theses: the stronger, that acceptance is sufficient for understanding; and the weaker, that

acceptance is constitutive, but only necessary. Owing his argument against the stronger to

Paul Horwich, Hale points out that if acceptance were sufficient for understanding, then

we would be ‘opening the flood-gates’ on logical truths and connectives, since it is at least

conceivable that one might accept Tonk no matter how unintuitive the inferential rule

is. Consequently, Hale urges the weaker notion, that acceptance is ‘merely’ necessary. In

this way, there is compatability between this view of meaning and the restriction of the

viable inference rules to only those which are sound, as connectives like Tonk are shown

not to have a genuine meaning (what would it be like for someone to accept Tonk?), but

connectives like ‘if, then’ and ‘and’ do. This is not to say that ‘and’ could be assumed

unproblematically, like ‘if, then,’ but instead that a non-circular soundness proof, using

the minimal kit alone, could be provided for ‘and’ and this would count it as a genuinely

meaningful connective. However, what is needed now is a way to deal with those who

would doubt rules we want to protect.

The thrust of acceptance as understanding is that one who does not behave in ac-

cordance with the principle is mistaken about the logical belief in question, but potent

doubts often come from those who understand the belief in question. For instance, Vann

McGee’s proposal for a counter-example to modus ponens might be swiftly shrugged off as

the misunderstandings of a logical apprentice; but it is precisely his accomplishments and

thoroughness with the topic that warrants serious consideration of the so-called ‘counter-

example.’11 So, one might consider the following (of many other examples McGee provides):

I see what looks like a large fish writhing in a fisherman’s net a ways off. I

believe

If that creature is a fish, then if it has lungs, it’s a lungfish.

That, after all, is what one means by “lungfish.” Yet, even though I believe the

antecedent of this conditional, I do not conclude

If that creature has lungs, it’s a lungfish.

11McGee (1985)

25

Lungfishes are rare, oddly shaped, and, to my knowledge, appear only in fresh

water. It is more likely that, even though it does not look like one, the animal

in the net is a porpoise.12

The problem here—why one would not assent to the conclusion ‘if that creature has lungs,

it’s a lungfish’—is due to the nesting of conditionals. When performing a ‘translation’ of

beliefs or language into logic, arguments of the form pIf φ, then if ψ then θq, require one,

at least sometimes, to assent to the truth of otherwise unintuitive or implausible beliefs.

McGee reasons that this is because our own practices reflect a further ‘law of exportation’

which states that...

pIf φ and ψ, then θq entails pIf φ, then if ψ then θq.

and so there is a “tension between modus ponens and the law of exportation. According

to the classical account, which does not recognize any conditional other than the material,

both are valid; but we will not expect them both to come out valid on any nonclassical

account.”13 Hale addresses this sort of concern directly and concludes that if someone

can intelligibly raise the doubt to begin with, then really the thing they assented to and

accepted was never quite the thing so doubted.14 In this case, that the doubt was never

about classical modus ponens, but about our non-classical use of natural language and the

relevant conditional operator for that.

So, regarding McGee’s counter-example, we would say that there is an unrestricted

version and a restricted version of modus ponens, where the restricted version cuts off

those arguments which would “essentially involve as major premises conditionals whose

consequents are themselves conditional.”15 Then, any doubt about modus ponens will

be of the unrestricted version, and what was really meant by modus ponens was the

appropriately restricted version all along.

This certainly gets one around the problem: any genuine doubt means you never

had genuine meaning for the thing doubted to begin with; but it is difficult, then, to

see how this principle might help address Carroll’s Tortoise. Given the type-2 skeptic,

12McGee (1985), pg. 462-46313McGee (1985), pg. 46614See: Hale (2002), footnote 1815Hale (2002), pg. 291 in footnote

26

we either shrug them off as not understanding the principle in question, or we admit

their hesitation but claim that the principle so explicitly stated was never the principle

in question. Behind every explicitly stated rule that could be questioned would be the

unstated and ‘real’ meaning. In practice this might likely not amount to anything,16 even

if one was to move towards another method of fixing the meaning—be it truth conditions or

‘conditions of correct assertion’—it would not change the fact that certain logical concepts

were of conceptual necessity ; but it would leave open the curious fact that those logical

beliefs taken to be a priori and necessary are subject to change, insofar as we thought we

made reference to them, ‘later.’17 This, however, should not be seen as fatal to Hale’s

position, only that it raises some discomfort given the seeming ineffability of those very

concepts we take ourselves to be entitled to.

This discussion raises one further point; namely, that Hale presents two distinct

projects that one might attempt to solve:

A : Explaining how we can come to know that basic rules such as modus ponens are

sound.

B : Explaining why it is not possible intelligently (i.e. clear-headedly and coherently)

to doubt the soundness of basic rules such as [modus ponens ].18

The principle of ‘acceptance as understanding’ only seriously applies towards project B.

The ‘ineffability’ so discussed, exposes the inability for our assent through practice to

explain how we grasp logical concepts; but this is really no price at all to pay, it was never

Hale’s intent to have the principle of acceptance as understanding solve all of the issues.

So far, then, we’ve seen this non-rule-circular position make quick work of the issues at

hand; however, our type-1 skeptic will require a little more effort to handle.

In the following section I will spell out how Hale might come to answer this skeptic,

but also what problems this commits us to; and particularly, I will show that we are left

with an IOU that is no better off than Boghossian’s. Then, in section 2.3 I will attempt to

relate Hale’s position to a broader category of positions called “default-reasonable beliefs.”

16Indeed Hale seems to think so when he claims that everything in the paper following his discussion ofMcGee could be “recast” to the better formed resrictred modus ponens.

17Say, by further reflection, or even a posteriori experience.18Hale (2002), pg. 289

27

In doing so, one may note that the narrow discussions thus far are more broadly applicable

than they first appear. Finally, in section 2.4, we will take stock of what issues are on the

table and where progress may be made.

28

2.2 Intellectual Recognition

Before setting off into the nuances of Hale’s theory, it is worth asking why the type-1

skeptic may not be immediately answered by the ‘acceptance as understanding’ principle.

If the type-2 skeptic could be disregarded as not knowing what they were talking about

when they claimed to understand modus ponens but refused to assent to its conclusion,

then why can’t one say the same for the type-1 skeptic who refuses to accept modus

ponens to begn with? Recall, that in the discussion of Boghossian, the type-1 skeptic’s

doubt could be understood as a question about whether or not the rule in question was

genuinely meaning constituting. If what makes a rule meaningful is just one’s acceptance

of it, then we run into the strong view that Horwich criticized; and if we go with the

partly necessary view that Hale proposes, then there must be some further way of fixing

the meaning.

Here is the crux of the issue—for if Hale were challenged, ‘and why modus ponens?

how is modus ponens “genuinely meaning constituting”?’, there is no clear story. Surely

introduction and elimination rules would play a part; one’s acceptance of the rule (and

so the behaviour that shows acceptance); and the aspects of the rule that might make it

conceptually necessary, i.e. its soundness; but seemingly the picture that these conditions

give together still does not provide a clear answer to our type-1 skeptic, for, I argue,

this instance of the skeptical worry is pushing on a prior step in the argument. Unless

one can provide a positive argument for modus ponens, then the negative argument (that

it’s soundness could not be doubted), will do little to unseat the skeptic—if they take

themselves to know some other connective, then why should they abandon their logical

system? And this is, in effect, to push on Hale’s first project, ‘project A.’

Unfortunately, there is no quick answer. Hale ‘shelves’ the question of how we may

come to know logical soundness, banking on the hope that in answering ‘Project B’ we

may come to have some idea of how to make progress.19 So, then, what is the supposed

lesson of project B?

I propose that there are two ways of understanding Hale’s argument: on the one hand,

and closer to the spirit of Hale’s paper, there is something particularly special about those

19Hale (2002), pg. 290

29

rules which appear in our minimal inference kit, and we come to know of these rules ‘first;’20

on the other hand, the relevant logical facts are, in a sense, ‘beyond us’ and so the sort of

knowledge that we are talking about is the high bar we never really obtain.

The second interpretation is quite a liberal reading of Hale. Indeed, it is so far from

the thrust of the paper, that it barely could be seen as the same position; but, it is worth

mentioning, if only to note the landscape of available positions. In saying that logical

facts are ‘beyond us,’ what is being noted is that the conditions of generality and necessity

make logic transcendental. Perhaps it is true that “some of us, at least some of the time...

are inclined to believe that we know” some logical fact,21 but a minor lesson that could

be had from Carroll’s Tortoise, Tonk, and discussions around the justification of logic, is

that this feeling of certainty, of knowing, is contingent to our practice. Alerting one to

a possible counter-example, or asking them to justify their use of some taken-for-granted

logical inference, brings about a whole suite of behaviour—constructing proofs, providing a

rule-circular argument, attempting to find further counter-examples, performing a reductio,

etc.—which Hale recognizes as being unsatisfactory for showing how we have the knowledge

we do. Thus, the position would look something like this:...

The minimal inference kit is no more special than any other and the fact that

it is indispensable to proving soundness is an interesting property which may

be used to explain why it is more difficult (maybe so much more so it seems im-

possible) to doubt than any other set of inferential patterns. It may be the case

that, for example, we are beholden to conceptual limits—just the ones that map

to the logical facts—but this will do little for explaining any sort of ‘knowledge,’

since we are not reasoners ‘in the limit.’ One’s doubts about logical facts are

entirely reasonable insofar as we have no special access to the transcendental

20To spell this notion of ‘first’ out a little more: In some sense, because the minimal inference kit rulesare indispensable to our reasoning about (minimally, the soundness of) any other logical idea, there willbe very little to any epistemological story before this inference kit comes into play. Perhaps we might havecertain intuitions or beliefs which are otherwise unconstrained, but once we talk of knowledge, however wemight attempt to do so, these inferences will come first. Thus, the goal is to tell a story which ensures thatonce we can say some agent has knowledge (at least of anything general or conditional), then whateverthat knowledge may be, it comes with the minimal kit—whether that means that prior knowledge of thekit was used, or that the agent learned both things simultaneously, or that there was never any otherphysical possibility, that we just do think with those rules that are of conceptual necessity.

21Hale (2002), pg. 279

30

truths. In just the way that genuine doubts expose our accidental reasoning

about the meaning of connectives, ‘acceptance as understanding’ shows we are

mistaken about logical truths given our inability to reason transcendentally;

yet, all but the most unmovable skeptic will accept the overwhelming amount

of logical practice and argument that we can contingently provide.

Now, though the above interpretation is entirely made up of the key ideas of Hale’s posi-

tion, one can see where the divide lay: this doesn’t seem to give us knowledge at all! That

our practices are moved by the invisible hand of logical reason seems to explain away the

possibility of knowing otherwise without telling us that we actually know anything. Fur-

thermore, Hale finds that “appeals at this point to self-evidence or to rational insight—to

a supposed capacity to discern things by the light of reason—... seem to amount to rela-

beling our problem rather than making a significant contribution towards its solution.”22

How else, other than the light of reason, might one close the gap between transcendental

conceptual limits and actual reasoning practice? This leaves us then with the first inter-

pretation, that there really is some priority to those inferences in our minimal kit, and

that they will then figure in an epistemological story somehow and before other sorts of

knowledge.

It seems to me that there are a variety of such epistemological stories which would

get at something similar to what Hale is looking for, but Hale concludes the paper with

the thought that there may be no inferential ‘gap’ between explaining how something is

impossible to be doubted and how it can be known (there would certainly be a gap, just

not one so structured by inferential reasoning), and that, instead, we may bear out the

conditions for knowledge in terms of beliefs: “To know that p is to have a true belief

that p and to be entitled to that belief... she may satisfy the entitlement condition by

believing something it is impossible—and so impossible for her—rationally to doubt.”23

Of importance to note about this condition is the fact that the impossibility of doubt is

not relative to the believer, it is a fact beyond the believer that they cannot doubt p and

so it is this fact which independently justifies, or gives entitlement to, the belief; and so

too, it should be noted, is the fact that p is true. So, Hale has provided a justificatory

22Hale (2002), pg. 28423Hale (2002), pg. 302-303

31

framework for individual’s beliefs which, in a sense, does not actually rely on their believing

at all. Universal quantification and conditional inference seem to fit the bill on true and

undoubtable beliefs, but this is still no story at all about how we come to these facts.

Earlier in the paper, Hale quietly attempts to address part of this concern. In a foot-

note attached to the discussion of the proof of Tonk’s being unsound, Hale ponders by what

right we can claim the truths of premises [3.] and [7.]24 Though their truth may be “obvi-

ous,” providing a compelling answer of how we know this is problematic. Hale considers it

implausible for knowledge of their truth to be got inferentially, for “quite apart from the

difficulty of coming up with any even remotely plausible premises from which such state-

ments might be drawn as conclusions, it seems clear that any such inferential answer would

set going a vicious infinite regress, of a piece with that into which Carroll’s wily Tortoise

enveigles the unwary Achilles.”25 The idea here is precursor to the point of indispensabil-

ity, and so the infinite regress cited is just the sort found in a rule-circular argument. This

said, Hale also forwards some preliminary commentary on how we may know the truth of

the inference in question; particularly, that he “can see no alternative to acknowledging

that what is involved here is a species of non-inferential intellectual recognition—which we

may as well call rational insight, and which has an indispensable role to play whenever we

operate with rules of inference.” This is not meant to be taken in quite the same way that

sense-datum theorists will claim perception is non-inferential, but instead, is restrictively

taken to mediate “recognition of particular inferences as exemplifying general rules.”26

So, how might this ‘restricted’ rational insight help in getting us from our believing

to conceptual necessary facts? If, as Hale indicates here, it is a merely a piece of rational

thought that we may move from particular instances to generals, and from generals to

particulars—that is, employ universal quantification—then we have some way of framing

our beliefs in accord with the sort of conceptual general necessity that logical facts are

taken to have despite the nature of our contingent and non-transcendental thought;27 but,

24For the reader’s reference:

[3.] The inference: ‘p, so p tonk q’ is of the form ‘A, so A tonk B’

[7.] The inference: ‘p tonk q, so q’ is of the form ‘A tonk B, so B’

25Hale (2002), pg. 298, footnote 24.26Hale (2002), pg. 298, footnote 24.27And one may note here that this is is now a reading much closer to the one we inititally took to be

32

it would seem, this also takes us far away from the humble characterization of indispensable

already taken on board. It is no longer just that we cannot doubt universal quantification,

but instead that the overall characterization of thought depends upon this ‘minimal kit.’

Now, perhaps, our minimal kit is even smaller than supposed and what we have really

landed upon is a new criterion with less baggage; but this would be to confuse the role of

the claims. The ‘minimal kit’ arose as those connectives which we had to assume on pain

of circularity. To say that our recognition of logical facts depends upon just the inferences

we cannot doubt, precisely because we cannot doubt them, and we cannot doubt them

because we recognize, in argument, their indispensability, precisely because of the logical

facts uncovered in the process, is as circular as any inferential argument.

What then, is the type-1 skeptic left with? It would seem, an IOU on how we come

to know conceptual necessities. Just as with Boghossian, the rest of the picture may hang

together nicely enough to address the type-2 skeptic and limit our connectives, at least

enough, to rule out Tonk, but the type-1 skeptic is given only an outstanding epistemolog-

ical story.

In the following section, the connections between the view just expressed here and

“default-reasonable beliefs” will be explored. Particularly, I will try to show that the

epistemological IOU is much the same as Hale’s and so we can begin to rule out an even

broader class of views which take this approach. Then, in the following section, we will

return to discussing the specific conclusions from the discussion of Hale in these past

sections, and Boghossian in the past chapter.

far from the spirit of Hale’s position.

33

2.3 Default Reasonable Beliefs

This section will draw comparisons between Hale’s view and the broader category of

views dubbed ‘default reasonable beliefs.’ I will attempt to show that the relationship

between ‘intellectual recognition’ and ‘default reasonableness’ functions quite the same way;

and so consequently, that the same issue with the type-1 skeptic will appear. Following

Boghossian’s characterization of “default reasonable beliefs,”28 they are those beliefs which

are “simply ‘default reasonable,’ reasonable in and of themselves, without any supporting

justification... It is reasonable to believe them, but not because there is some positive

ground by virtue of which they are reasonable.”29 In other words, they are beliefs which

are justified because they are prima facie reasonable—no more and no less need be said.

Though this is not a fundamental part of the position, Boghossian continues to spell out

his take on it by appealing to a further condition on grounds of plausibility; particularly,

that the sort of justification such beliefs are given is that they are “presumptively but

defeasibly justified.”30

Now, Hale certainly never indicated that anything could serve as a basis for logical

knowledge. To claim that would be an interpretative mistake of the highest degree; but

what discussion of “intellectual recognition” reveals is that we have justification for be-

lieving in universal quantification, for example, due to it’s ‘rational obviousness’—little

positive ground indeed. That said, Boghossian’s initial characterization is attempting to

pick up on what he takes to be a broader strategy or trend among many others, and so

there are a variety of ways we might take something to be default reasonable...

1. “A default reasonable belief is any belief which, by virtue of being presupposed in

any justification that a thinker might have, is neither justifiable nor refutable.”

2. “Beliefs that are default reasonable are those beliefs that a thinker finds ‘self-evident’.”

28His discussion of the matter does a good job of joining together many positions. There are others,particularly Hartry Field, who discuss the issue more directly and ‘on its own terms;’ but their summaryis less rhetorically useful and raises many further concerns. We will return to Field in Chapter 3 whendiscussing non-factualism, and there some of his views on default reasonable beliefs will also be presented

29Boghossian (2000), pg. 23830Boghossian (2000), pg. 238-239.

34

3. Default reasonable beliefs are just those beliefs “such that, having those beliefs is a

condition for having one of the concepts ingredient in them.”

In these three accounts, Boghossian casts a wide net for what may be considered a ‘default

reasonableness’ approach to the justification of beliefs. I will not take any of these to be

‘the canonical approach,’ but it can be seen that some of these are more, and some less,

amenable to Hale’s approach—there is a family resemblance between all the positions.

The first characterization gives us one condition by which some belief is default rea-

sonable: that the belief be ‘presupposed in any justification a thinker might have;’ and,

by consequence, the standing of this belief then is ‘neither justifiable nor refutable.’ We

might see this as very closely related to Hale’s own position, as the sorts of beliefs which

are undoubtable, those within our minimal kit of inference, are the ones that we can use to

supply justifications for other logical concepts (via soundness proofs), and which cannot be

refuted (doubted), or justifed themselves (since this would invoke circularity—using modus

ponens to prove the soundness of modus ponens).

There is a further way of understanding how a belief may be ‘presupposed in any

justification’ and this would make this view of default reasonable beliefs closely related to

indispensability. One might, for example, take ‘any justification’ to include those justifica-

tions which fail, or the general acts which, through their performance, grant justification.

Stretching this understanding then, one is only a ‘stone’s throw’ from the idea that this

condition is really calling for those beliefs which are presupposed in our most general

thought—those beliefs which are indispensable to our thought. Wright forwards a clear

conception of this when claiming “a proposition [is] a cornerstone for a given region of

thought just in case it would follow from a lack of warrant for it that one could not ra-

tionally claim warrant for any belief in the region.”31 Cornerstones here are those beliefs

which we could then not do without. Note, however, that this is both a far different view

from Hale’s and a much stronger reading of the default resonable condition.32

Hale is not after the idea that we literally cannot think without some logical concept,

some conceptual necessity—certainly acceptance as understanding shows that we are not

31Wright (2004), pg. 167-16832There is some promise for indispensability to answer the type-1 skeptic, and we will see this come

about again in chapter three, but not in the way implicated here. To fully discuss Wright’s conception ofcornerstones is far out of the scope of this thesis.

35

ideal reasoners and can misunderstand logical concepts—only that we cannot rationally

doubt those certain concepts. And here is why the skeptic’s challenge remains: there

is some non-inferential gap that must be jumped to get to knowledge of these logical

concepts,33 and without this explanation there is no ‘positive ground’ to make one employ

modus ponens, quantification, or whatever else might be in the minimal kit.

What of the idea that beliefs are default-reasonable just when some thinker finds them

‘self-evident?’ I take it that there are two ways of discussing this; namely, charitably and

uncharitably. The uncharitable reading would literally have it that any belief could be so

justified so long as there is someone who is willing to think it evident. Consequently, we

would be discussing a position whereby no belief is ruled out prior to investigation as there

is no principled way to distinguish them—one could always imagine a person who could

possibly believe the idea in question no matter how unjustifiable it seems to anyone else.

Whether or not there is a person who then assents to some particular belief will be our

basis for claiming the belief so justified, but otherwise, one would have to remain agnostic

about the rest. Yet, if Tonk seemed problematic because it allowed us to pass from any

premise to any conclusion, because it forces us to accept that every sentence is true if any

sentence is true, one should be similarly skeptical of the position that all beliefs are either

justified or not not justified. In any case, this is the less interesting of the two readings:

what then, is to be made of this idea if we are charitable interpreters?

It would seem as though there must be some reading of ‘self-evident’ which is not

so ‘radically subjective.’ For example, we might take self-evident to mean undoubtable;

and if this is the case, then what we really have is Hale’s position (and the problems that

come with it). By virtue of one’s intellectual recognition they have afforded themselves

the minimal inference kit, which is neither justifiable, except just in virtue of their intel-

lectual recognition, nor refutable, since the belief in question is of conceptual necessity.

Another strategy might be to take self-evident beliefs to be constrained by some sort of

plausibility condition, like Boghossian’s suggestion for their being “presumptively but de-

feasibly justified.” However, this would take us closer to the uncharitable reading and so

33There may be hope for merging this view of default reasonable beliefs with a rule-circular argument forjustification, but as we saw with Boghossian’s positions, even this ‘inferentialist’ approach will not satisfythe type-1 skeptic. The view may be default reasonable, but only to the extent that it’s being presupposedis because of its being genuinely meaning-constituting.

36

raise concerns about what is really significant in claiming some beliefs being so justified.

There is potential in this argument if one can provide a set of critera by which logic may

be empirically overturned, but I will not take this discussion up here. What can be said

is that, at the least, this is no obvious position and that if logical concepts are the sort

that Hale outlined, of conceptual necessity, then it is difficult to see how they may ever be

defeasible.34

This leaves Boghossian’s last characterization of default reasonable beliefs; that they

are those beliefs such that “having those beliefs is a condition for having one of the concepts

ingredient in them.” The idea here is that for one to even be said to have the belief in

question, they must “believe a certain proposition containing it.”35 In the case of the

conditional, for example, this would mean that for one to have the logical concept of ‘if,

then,’ then they must also have, or assent to, further beliefs, like logical implication or

the validity of modus ponens, that ‘contain’ the conditional. Or, in Boghossian’s words,

this would amount to the claim that “anyone possessing the concept of conditional would

have to have the belief that MPP is a valid rule of inference.”36 There are, at least, two

important things to note about this.

First, this is a very similar sort of condition to the principle of acceptance as under-

standing. Hale’s idea was that if you did not accept the consequences of the conditional

then you could be said to have misunderstood the conditional to begin with. Here the

idea is that if one does not take on board the consequences of some belief, or necessary

associated properties, then one never really had the same belief in mind to begin with.

However, this leads us to the second important point: this condition was extremely ef-

fective at warding away type-2 skepticism, and largely ineffective at warding away type-1

skepticism. Indeed, Boghossian echoes this concern when he says:

“Surely, one can have and reason with conditional without so much as having

the concept of validity or of logical implication. At most what the theory of

34For the inclined reader, Boghossian provides a discussion of this sort of defeasibility in the context ofthe Quinean account of logic (See: Boghossian (2000), pg. 232-234); Hartry Field provides an extensivedefense for logic as the sort of thing which could not ever be empirically defeasible in Field (1996) and wewill discuss his view further in chapter 3; and finally, Nenad Miscevic defends a view of an a priori logicwith a posteriori defeasible justification in Miscevic (2012)

35Boghossian (2000), pg. 24036(Boghossian, 2000), pg. 240

37

concept possession would license is that inferring according to MPP is part of

the possession condition for conditional, not the belief that MPP is valid. But

what we are after now is the justification for the belief.”37

In this way, default reasonable beliefs with possession conditions might be an apt way to

describe the function of the principle of acceptance as understanding in Hale’s view, but

it would fail to add anything more to the picture—the type-1 skeptic is looking for the

justification of the belief, some positive ground for the belief.

It would seem then that ‘default reasonable beliefs’ does not aid Hale’s view in ad-

dressing the type-1 skeptic (and so, alone, does not address the type-1 skeptic either).

Furthermore, we can see how the epistemic picture provided by Hale is similar to that of

default reasonable beliefs generally. In the following section we will take stock of the criti-

cisms of Boghossian and Hale, and where we have done better or worse at addressing this

thesis’ guiding issues; and then in chapter 3 we will discuss Hartry Field’s non-factualism

which will bring about, among other ideas, default reasonable beliefs and empirical defea-

siblity once more.

37Boghossian (2000), pg. 240

38

2.4 The Morals So Far

At this point much ground has been covered, so I would like to briefly restate some of the

positive conclusions and then make some remarks about how we are faring with respect to

our guiding issues.

Lesson 1a: Rule-circularity fills an important niche by conferring warrant to some conclusion

through its explanation of the involved inferential rule. Recall (RC): “S’s rule-circular

argument for a rule of inference M will confer warrant on S’s belief that M is truth-

preserving, provided that M is a genuinely meaning-constituting rule for S.”

As we saw earlier, rule-circular argumentation dealt well with the type-2 skeptic: one

could appropriately ‘discharge’ the infinite regress of hypotheses once one application of

the rule was accepted. And furthermore, the issues that came with rule-circularity were

rather to do with the attempt to spell out “genuinely meaning-constituting” in terms of

conceptual roles.

Lesson 1b: The positions discussed were not fundamentally opposed to this narrow use of rule-

circular argumentation—explaining the justification of our rules rather than per-

suading another to use them or explaining their origin. In other words, they do not

contain, implicitly or explicitly, principles like (NoRC).

Hale certainly hoped to avoid rule-circular argumentation and posed three concerns for it;

however, it was not clear that these criticisms were effectively posed with respect to the use

of rule-circular argumentation given by the principle (RC). Nor was there any indication

that the various default reasonable beliefs approaches would bar one from later justifying

their logical conclusions via rule-circular arguments. Now there is one further ‘lesson’ to

note, but it will require some further explication.

Lesson 2: It is not clear that there is any problem with taking the meaning of a connective to

be given by its introduction and elimination rules.

Of course, this is a bold claim and marks a significant departure from the literature

discussed so far, but it is, I will presently attempt to show, correct. The immediate response

39

would be to claim that Tonk has introduction and elimination rules, but is clearly a ‘bad

connective’—certainly this is the attitude we have taken throughout the thesis and a point

to be upheld—and so a rule’s being “analytically valid” does not give it a genuine meaning;

however, it is this latter point that is not so obvious. A rule may have a genuine meaning

and yet still be a ‘bad rule’ to employ. To better spell out the option under consideration,

Boghossian’s and Hale’s arguments against Tonk should be briefly reconsidered.

On Boghossian’s account, Tonk was a problem to be dealt with because rule-circular

argument seemed unconstrained—there was no other method to justifying logic and it

appeared that we could provide a rule-circular argument for Tonk—and this was circum-

vented by the condition of “genuine meaning” in (L) and (RC).38 One was entitled to infer

by a rule so long as it had a genuine meaning, and one could then justify their inferred

conclusions in accordance with that rule by supplying a rule-circular argument. One may

note, however, that this is only one way of restricting rule-circular arguments and was

strategically chosen for Boghossian’s ‘point-to-come’ about conceptual roles. If conceptual

roles determine the meaning of a rule, then we have a ‘clear path’ from epistemology of

conceptual roles, to entitlement, to warrant. But (L) and (RC) need not share the same

restriction (and as we saw, ‘conceptual roles’ were not without their issues). It may be

that, for example, (L) requires a meaning restriction and (RC) requires a soundness restric-

tion.39 If we take this point in conjunction with the idea that introduction and elimination

rules function fine for determining meaning, then one would be entitled to infer according

to Tonk but not be justified in the conclusion of any Tonk argument.

In Hale’s position we saw a concern for the meaning of connectives to come out in terms

of the necessary but not sufficient condition of one’s acceptance of the logical concept. Tonk

was ruled out because assent to Tonk alone is not enough to give it a genuine meaning

(‘what would it be like for someone to accept Tonk?’) and the ‘minimum bar’ for a

38For the readers reference:

(L) : If M is a genuinely meaning-constituting rule for S, then S is entitled to infer accordingto M, independently of having supplied an explicit justification for M.

39Here then, (L) would stay the same and we might amend (RC) like so:

(RCS) : S’s rule-circular argument for a rule of inference M will confer warrant on S’s beliefthat M is truth-preserving, provided that M is a sound rule.

40

connective would be, instead, its being sound.40 But here one may then note that Hale

was perfectly capable of making sense of Tonk-statements, even proving things about Tonk

(specifically, its unsoundness). What qualities Tonk lacked, and so why it was ruled out

as a bad connective, was ‘conceptual necessity’ and soundness. The question then is, to

co-opt Russell’s distinction: is it possible to differentiate between assent to one’s reference

of a rule,41 and assent to one’s assertion of a rule? Is it possible to differentiate between

genuinely meaningful but not justified uses of a logical concept, and genuinely meaningful

and justified uses of a logical concept?

There is a way in which the questions just posed are useless: ‘of course there are

things justified and things not justified;’ but the arguments posed by Hale and Boghossian

seem to imply that once one ‘has’ a logical rule, license to a particular inference, then they

are justified. And this will be just because one could not ever be licensed to a Tonk-like

inferential pattern. Maybe, once harassed by a pesky Tortoise, one will have to produce

a proof or argument which shows their so being justified, but this a mere inconvenience.

Consequently, the challenge here is to say that one might be properly entitled to all sorts

of logical connectives on the basis of there being appropriate introduction and elimination

rules, but that they would not be justified for any particular actual inference without

meeting some further criteria.

The next chapter will focus on Hartry Field’s non-factualism in an attempt to make

further headway on our guiding problems. Particularly, I will show how some form of rule-

circularity is invoked in Field’s framework for justification and also how a different view

of meaning, and so Tonk, is presented; particularly, one more amenable to the discussion

just above.

40There is a sense here in which Boghossian and Hale are actually striking upon the same idea. InBoghossian’s case we had to be careful to note that not all logical ideas we reference, like Tonk, might haveconceptual roles (though he does no provide any criteria for when they may); and in Hale’s case, we areurged to recognize that though we can assent to all sorts of ideas, only some of them will be of “conceptualnecessity.”

41Russell uses the language of “asserted” and “unasserted,” or “considered,” and compares this to thegrammatical notion of a verb and a verbal noun. I use “reference” here to capture these ideas succinctly andhopefully not to implicate the psychological aspects, which Russell also hopes to avoid, that ‘consideration’may bring to mind.

41

Chapter 3

Logical Methodology and Non-Factualism

This chapter will follow quite the same structure as those previous: I will introduce Field’s

non-factualism, then I will attempt to show how the view does or does not address our

guiding issues, and then bring to the fore any particular residual problems. Since Field’s

non-factualism is an encompassing epistemological view which tackles many issues, the

discussion will be broken up into three sections. The first will explain to what extent Field

takes logic to be an a priori matter and will discuss his distinction between those beliefs

which are weakly a priori compared to properly a priori. The second will explain the role

of an ‘evidential system,’ and how Field takes such systems to be related to our epistemic

‘goals.’ And finally, the third section will explain how deductive logic is justified given

the other commitments. Particularly, I will attempt to show that Field makes a case for

deductive logic being indispensable to our otherwise inductive reasoning, which is itself

indispensable, and that subsequently there is the form of a rule-circular argument.

42

3.1 A Priori Logic, Weak and Strong

It was noted briefly in the discussion of Default Reasonable Beliefs that Boghossian was

not their only commentator, and indeed Field has addressed default reasonable beliefs quite

directly. Particularly, in “Apriority as an Evaluative Notion,” he characterizes such beliefs

as those which are weakly a priori: that is, those “that can be reasonably believed without

empirical evidence.”1 So, for example, it might be default reasonable to believe that the

conditional operator is valid; but, so too might be the proposition: ‘people usually tell the

truth.’2 Of course, these two beliefs are worlds apart, but one can see how each might be

plausible without some prior empirical inquiry.

On the other hand, there are those beliefs which are, so to speak, a priori without

qualification (and which I will call ‘properly a priori’),3 and this is a matter of their

satisfying a further condition; namely, their being empirically indefeasible. So, for Field,

properly a priori beliefs are those for which no empirical evidence may overturn their truth.

Consequently, all properly a priori beliefs are weakly a priori, but only some weakly a priori

beliefs will be properly a priori—just those that are empirically indefeasible and plausible

without empirical evidence to begin with.

In the case of “people usually tell the truth,” we have a belief which is a priori in

the weak sense: it is plausible to believe without some empirical study or experience first,

and if some empirical study were done, it may very well be the case that the belief was

overturned, that one found that people do not usually tell the truth. Now, the principles

of deductive logic are certainly weakly a priori in that they are plausible to believe without

a posteriori inquiry, but it is less clear whether or not beliefs in logic principles could ever

be overturned. What way would the world need to be to make a belief in, say, universal

instantiation, wrong?

To spell out Field’s view on this matter will require explaining two points: (1) that

there is some sense in which empirical matters affect logic, but that this does not make

1Field (2000), pg. 1172Field (2000), pg. 1203Field wavers on calling these concepts ‘strongly a priori’ and opts instead for simply, ‘a priori.’ The

reader may ignore the addition of ‘properly’ if they so choose, as it is only used for clarity, to denote thosebeliefs which are both weakly a priori and empiricially indefeasible.

43

them empirically indefeasible; and (2), that there is some sense in which logic is defeasible,

but not empirically so. Regarding the first, Field is particularly interested in the debate

surrounding quantum logic:4 might there ever be a reason for us to abandon classical logic

in favour of quantum logic? There is the immediate case of quantum phenomena which

appear to be measurable and real instances of physical situations which, when translated

into logical propositions, fail to cohere with distributivity laws. However, it is not clear

that such phenomena disprove classical logic, or logics which assume distributivity, or even

the notion of distributivity itself, for such claims do not depend on physical phenomena in

the first place.

Regarding the second point, there is a sense in which logic is defeasible; particularly,

it is conceptually defeasible. On this matter, Field says...

“I am not saying that we can completely dismiss the possibility of replacing

standard logic with a ‘quantum logic’ in which the distributive law is aban-

doned, and of arguing that one of the attractions of this logic over classical

logic is that it would make quantum phenomena less mysterious: that would

be dogmatism. But there are considerable conceptual obstacles to working out

of what it would be like to employ such a logic. For instance, there are obstacles

to explaining the circumstances under which special distributivity assumptions

can be invoked...; and there are obstacles to explaining what the inductive

methods that would go with such a logic would be like... We can’t completely

dismiss the possibility of replacing standard logic with nondistributive logic,

because we can’t completely dismiss the possibility that these conceptual ob-

stacles can be overcome. But overcoming them would be largely a conceptual

matter, not an empirical matter.”5

There are a number of things to take note of in this passage—particularly, the meaning

of those two options which are considered as conceptual obstacles, points we will see in

the coming sections—but I will focus just on the broad idea here; namely, that there are

conceptual obstacles to our use of a priori concepts, and in this case logic.

4See, at least: Field (1996), Field (1998), or Field (2000)5Field (1998), pg. 15

44

The view under consideration here would have it that properly a priori concepts could

not ever be wrong a priori, but that there may be issues with the way that we use them;

and this will be the product of our own conceptual mistakes. This amounts to, in effect,

Field’s idea that “the so-called logical truths are indeed true in the most straightforward

sense; the claim that belief in them is strongly a priori justified, on the other hand, is an

evaluative claim.”6 This is not to say that those beliefs, in say, logic, are not properly a

priori, or strongly a priori, only that having them does not provide any such justification.

If they were so justified, then it would be difficult to see how they may be defeasible,

conceptually or empirically.

In sum, Field would have it that logical concepts are properly a priori, they are plausible

without empirical grounds and empirically indefeasible; but, they are not undoubtable.

Consequently, they may be ‘revised’ in response to conceptual issues, and this will amount

to a change in our epistemic practice with those concepts—and, perhaps, our being justified

or not in using them—rather than an apt response to a recognition that they are not true.

6Field (1996), pg. 370

45

3.2 Evidence and Contingent Reasoning

One issue with the first ‘conceptual obstacle’ raised above is the vagueness about what

is meant by “circumstances,” and then how these circumstances affect the applicability of

concepts (especially those we take to be properly a priori, and so true always). However,

Field presents the notion of an evidential system: “a bunch of rules governing what to

believe in what circumstances.”7 Consequently, we can see that the question of ‘under

what circumstances can certain assumptions be invoked’ will depend on one’s evidential

system, the norms or rules they assent to which determine which concepts they believe in

which circumstances.

Of course, this does not completely clear up the matter as one may then pose the

question, among others, ‘how do we get our evidential systems?’8 There appears to be a

circular issue if evidential systems determine what to believe in certain ‘circumstances,’

but those ‘circumstances’ determine the evidential system. For example: if one is dealing

with quantum phenomena, quantum circumstances, and this determines their use of a

non-distributive logic, but that use of the non-distributive logic then determines what to

believe about the quantum phenomena, then it would seem that there is only one possible

thing to believe. Or, it could be that there is but one evidential system always employed

by all people at all times, but this is not the picture that Field has in mind.9 Evidential

systems are themselves contingent, but not upon the circumstances for which they tell us

what to believe; instead, they are relative to our epistemic goals.

Field buries this notion amongst further discussions of externalism, reliablism, natu-

ralism, and so forth, and never quite explicitly states it as such; but a number of passages

support this idea, and particularly, the following:

7Field (1996), pg. 3628I take it that another important and immediate question is, ‘how do I know what someone else’s (or

for that matter, my own) evidential system is?’ Field proposes that this is an idealization, an evaluation,and not a properly factive question: “To ascribe to a person an evidential system is to give an idealizeddescription of his or her belief-forming and belief-retaining behaviour.” (Field (1996), pg. 362) If justifi-cation in Field’s non-factualism were to depends upon our explicit knowledge of evidential systems, thiswould present a problem; however, we will see later how his approach to justification allows us to avoidthis issue.

9Nor, the reader may note, does it appear to present a compelling epistemic story. How do we recognizethis system? How do we come to know we have the system? Perhaps, through intellectual recognition...

46

“A first advantage of this non-factualist approach is simply that we have some

idea how to go about deciding whether to employ an evidential system with

certain features...: what is involved in deciding to employ a certain sort of

evidential system is seeing how well such a policy would accord with one’s

epistemic goals.”10

And so, the circularity noted is avoided. Evidential systems are relative to the epistemic

goals we have in mind—what we want to know about, and what epistemic values we

may have regarding our results (for example, expressive power or reliability)—and when

applied to the world, to certain circumstances, determine what we believe. For clarity’s

sake (particularly, when there are many goals in discussion) I will use the word ‘domain’ to

indicate those goals which specify what we want to know, and ‘goal’ or ‘value’ to indicate

those goals which specify certain qualities of our conclusions (i.e. that they are reliable or

powerful).11 One is not forced to use a certain evidential system, instead evidential systems

are relative to the epistemic goals one has, in the sense that which evidential system is the

appropriate one for us to use depends on which one best enables us to meet our goals.

One might be tempted at this point to claim non-factualism to be relativism on two

accounts: first, if our evidential systems are goal dependent and we do not restrict what

goals are permissible, then any evidential system would be allowed; and second, if logical

concepts are subject to change according to one’s evidential system, then we may be

inadvertently licensing one to infer by Tonk rules. The latter of these two points will be

discussed partially in the following section, and then again in different terms in section 3.4;

but the first may be addressed now.

Given the assumption that people select the best (or at least, plausibly good) eviden-

tial systems for their epistemic goals, then it would seem that, without restricting one’s

goals, there could be, in principle, goals that would call for evidential systems otherwise

considered questionable.12 For example, if we consider a potential epistemic goal to be pre-

dicting the future of one’s romantic relationships—to come to know, and assent to, those

10Field (1996), pg. 37711Field, unfortunately, provides no clear distinction of his own and uses goal to describe everything.

This is a feature of his theory, as it should help one to see the ever-dependent nature of methodology toprior epistemic dispositions, i.e. goals; however, discussion can become quickly confused without somelinguistic separation.

12One might be tempted at this point to say that people ‘ought’ to select the evidential system which is

47

relevant propositions—then we may license, as a plausible evidential system, the practice

of tea leaf reading. Tasseography, at least, has a history of such predictions.

That said, it is not clear that we are allowing one to infer by tasseography always ;

but rather, there is a set of goals, pertaining to what we may know or what qualities of

that knowledge we may value, which tasseography will sometimes be better suited for and

sometimes not suited for at all. If a cosmologist were to attempt to predict one’s romantic

relationships, for example, then one might be far more skeptical of their conclusion than

they might be of, say, their fortune-teller’s conclusions. In other words, there may be epis-

temic goals we have for which there are no apt methodologies—practices which do signifi-

cantly better than chance—and so, relative to those goals, otherwise reliable methodologies

(cosmology) do no better than otherwise poor methodologies (tea leaf reading). So, this

does not generally undermine the cosmologists inferences or reliability in other domains, it

shows that evidential systems, and broadly, theoretical apparatuses, are evaluated relative

to, at least, their domains.

One might note that there also appears to be a difference between so-called ‘radical

relativism’ and the sort of relativism which is a consequence of non-factualism, a kind of

moderate relativism. Field rhetorically asks when discussing default reasonable beliefs: “In

virtue of what is it reasonable to use modus ponens on no evidence?” and then concludes

that due to evidential systems being so relative,13 the proper question should be “why value

a methodology that allows the use of modus ponens on no evidence?”14 We may drop the

point about evidence here, for what is relevant to the discussion of relativism is that

whatever beliefs, principles, or evidential system, one wants to argue for, that argument

will be reduced to an argument about epistemic goals and how well that ‘methodology’

does with respect to those goals (here we might think of goals as domains), which may

itself implicate further debates about other meta-goals or tangential goals (and here we

might think of goals as values).

There are two supporting points to make about this—particularly, points which un-

best for their goals, regardless of whether or not they do (and so to avoid assuming anything about theirselection behaviour); but we will see that Field does not take there to be any such oughts.

13There is the additional point that Field takes there to be no straightforward matter of fact regarding“reasonableness.” There is only reasonable relative to an evidential system, to dispositions, to goals, or tothe evaluated ideal we construct for one another. See: Field (2000), pg. 127-128

14Field (2000), pg. 128

48

dermine the ‘scare’ of relativism: first, that there is actually a general reasonableness and

common ground to goals; and second, that the lack of a principled prohibition on certain

goals does not undermine the actual historical results that evidential systems produce.

Regarding the first, Field argues that one should recognize...

“That certain small modifications would produce results which have certain

advantages (as well as certain disadvantages) over the results [our evaluating

systems] produce. For instance, we recognize that a system slightly more strin-

gent in its requirements for belief is more reliable but less powerful. So we

recognize that a slight modification of our goals... would lead to a preference

for the other system, and we regard the alternative goals as well within the

bounds of acceptability. Consequently we make no very strong claims for the

preferability of our system over the alternative: the alternative is slightly less

good than ours given our precise goals, but slightly better on alternative goals

that are by no means beyond the pale.”15

The idea being that most goals can be seen as decently acceptable—with moderate advan-

tages and disadvantages—and that completely outrageous goals is largely a ‘boogeyman’

problem. However, Field does contest the extreme relativism (still in principle possible)

that might come with one who endorses some very questionable goals but concludes: “so,

what?”16 Indeed, the point of non-factualism is to call for a “goal-relative notion of better”

which would avoid the pitfalls of assuming that there are matters of fact about ‘standards

of correctness,’ and that if there are outliers (like the ‘Moonies,’ those who follow the word

of the Reverend Moon) they aren’t to be dismissed outright ; rather, those outliers who sub-

scribe either to vastly different epistemic goals or methodologies are to be argued against

with moral oughts, instead of epistemic oughts. And all this culminates in the point that:

“We don’t need to believe in metaphysical constraints to believe that [one has] got lousy

goals. (And if calling the goals lousy is evaluative rather than factual, so what?)”17

So, regarding Field’s second supporting claim, if all practices really were equal without

metaphysical constraint, then there would be no problem in so choosing to follow some

15Field (2000), pg. 14116See, Field (2000), pg. 140-14317Field (2000), pg. 140-143

49

methodology or set of goals;18 but, clearly, this is not the case. Some practices will ‘win out’

over time and“what makes scientific methods better isnt that they say that they will lead

to more truth and less falsehood than these other methods, it is that they do.”19 Maybe

prima facie all evidential systems and goals are permissible, but it would be a mistake

to think that, at least, some of these debates have not made progress over the course of

history, to think that tea leaf reading and science are still equally successful.

In a way, Field is conceding the point: non-factualism is a relativism; but to consider

this a fatal problem would be to forego the ‘point’ of non-factualism’s stress on evidential

systems, on engaging in a methodology—taking up some evidential system and using it in

the world—which will itself reveal its usefulness, or uselessness, over time. Then, Field’s

hope is to say that just because evidential systems are relative to goals doesn’t mean

that the question of, when comparing two evidential systems, ‘which system is better for

a particular set of goals,’ is without an answer. However, if logic is a properly a priori

matter, and so empirically indefeasible, then one may want to question how an otherwise a

posteriori view of the success of evidential systems relates at all to our major concerns—how

do properly a priori concepts get ‘picked’ as a methodology, and how do they ‘succeed,’ i.e.

lead to truths a posteriori? This brings us to the final section where I will discuss Field’s

view on the indispensability of logic to epistemology.

18At least, it is difficult to see how, or why, we might want to privelege one methodology over anotherif there is no relevant metaphysical claim or principle to compare them by.

19Field (2000), pg. 139-140

50

3.3 Universal Reasoning and Circular Justification

In the first section there were two conceptual obstacles introduced, the first being about the

circumstancial application of some concepts, and the latter being the explanation of ‘what

the inductive methods that would go with [non-classical] logic would be like.’ It is in asking

how, generally, properly a priori concepts might ‘win out’ in their application, as evidential

systems, that these two obstacles meet. If logical principles are an empirically indefeasible

matter, then how is it that we might use them in an evidential system and so empirically

corroborate them? This will introduce three further aspects of Field’s epistemology: (1)

the global use of inductive reasoning across evidential systems; (2) the circular justification

of those concepts used in evidential systems; and (3) the indispensability of deductive

logic. Subsequently, I will attempt to show that non-factualism provides a rule-circular

justification for a priori logical principles insofar as they are invoked in our evidential

systems.

The last section ended with the question: ‘in what sense do we inductively use properly

a priori concepts, concepts we take to be empirically indefeasible?’ Considering the history

of empiricism and debates about the a priori, at least, this would be a reasonable question

to ask; however, Field dumps this divide between a priori and a posteriori concepts when

supposing that we are fundamentally ‘probabilistic believers.’ Over time our confidence in

all of our beliefs is subject to change based on the application of our evidential system at

a particular time and the evidence with which we are confronted. This is not to say that

we are ideal reasoners, or fundamentally ‘Bayesian’ (as so many authors are wont to do),

but rather that all of our epistemic claims can be understood as probabilistic claims, even

those claims that we would otherwise effectively take to be non-probabilistic—i.e. those

claims which Hale might call undoubtable.20 In this way, there is no application of an

evidential system which will not involve inductive ‘updating.’

Before we turn to the question of how deductive logic can neverthless count as indis-

20More particularly, Field has in mind a fundamental conceptual scheme, given by a set of rules accordingto probabilistic axioms, which all further epistemic claims are couched in. For further detail, see: Field(1977). Unfortunately, to cover Field’s “probabilistic semantics” in depth is beyond the scope of the thesis,but the crucial point, that our semantics for all epistemic claims is probabilistic, is all that is needed toprogress.

51

pensible if we are fundamentally probabilistic reasoners, it can now be shown how Field’s

account justifies the conclusions of our evidential systems. This depends upon two ideas:

that evidential systems entitle one to those conclusions which are the consequences of the

system assented to, and that the reasoning behind our choice of evidential systems is rule-

circular. On this first point, Field suggests that “if a person’s evidential system licenses

the person to believe that p under certain conditions, and the person does believe that

p under those conditions, then the person’s belief is quasi-descriptively justified : justified

relative to the person’s own evidential system.”21 The choice of the evidential system,

that ‘methodology’ which will determine what someone ought to believe in certain cir-

cumstances, entitles one to those particular conclusions about certain circumstances which

follow from the reasoning implicated by the deductive principles assumed in the system.

Regarding the second point, however, it is more difficult to see how we might move from

a quasi-descriptive justification to an actual justification. Continuing the above discussion

about science and tasseography, Field says:

“What makes scientific methods better isn’t that they say that they will lead

to more truth and less falsehood than these other methods, it is that they do

lead to more truth and less falsehood than these other methods. In saying

that they do this I am presupposing the methods I accept, but that should go

without saying: that’s what accepting a method involves. Of course, this is

circular. (‘Rule-circular’, anyway).”22

To apply an evidential system is to suppose a set of principles and concepts, logical or

otherwise, which one then reasons according to. This is the “one step” that Boghossian

asks for—to even begin inquiry with an evidential system is to assent to the principles

in question. That said, Field is not entirely convinced by this partial picture he presents,

noting that rule-circular justifications do not seem to be worth much of anything if they can

never turn out false; and this would then seem to be a problem for our logical concepts if

they are the sorts of properly a priori things which could never be false. So, Field concludes,

“rule-circular ’justifications’ of our methods have another role: they serve to explain why

21Field (1996), pg. 362-36322Field (2000), pg. 139-140

52

we value our methods over competing ones.”23 This, however, does not take away from

the justification of any inferential rule for two reasons: one, we have actually provided a

stronger justification, a justification for the whole evidential system which includes that

inferential rule; and two, because one must still assent to the evidential system in question

before being able to be entitled in the first place (there is, in effect, a constitutive part of

one’s ‘accepting’).

So then we might bring all this discussion together to conclude that inductive reasoning

is always justified as it will be employed across all evidential systems. Moreover, it will

always prove to be better than its rivals, from an inductive point of view, and so will

have rule-circular justifications available for its basic principles. At least, Field makes this

point when he says that “our basic system of inductive rules is... ‘immodest:’ it positively

evaluates itself over it’s competitors.”24 What is now needed is a story which explains, in

whatever relation to inductive reasoning, why deductive logic will also be justified.

If deductive logic was necessary to employ our inductive reasoning then the picture

would be quite clear; however, it is not evident that Field takes deduction to be indis-

pensable in this manner. In, at least, “Logic, meaning, and conceptual role,” Field seems

to imply that inductive reasoning is actually prior to deductive reasoning; and that the

semantics for our logical connectives is understood with respect to probabilistic rules and

axioms.25 And so, if it were the case that deductive reasoning is second fiddle to inductive

reasoning, we might have no reason to suppose that deductive logic is indispensable or

ever justified in this rule-circular manner—every evidential system might employ induc-

tive reasoning (since all of our reasoning is in those probabilistic terms), but we need not

suppose that all evidential systems employ deductive logic. However, Field concludes that

it is not the case that “logic is ‘necessary’..., but rather that the epistemological princi-

ples that would do the licensing must themselves employ the logic in question. If logic is

regarded as up for grabs, there is no clear way to apply epistemological principles; there

is no clear fact of the matter as to what they license.”26 Given some set of principles, we

23Field (2000), pg. 14024Field (2000), pg. 143. Here, Field is also borrowing his terminology from David Lewis; particularly,

Lewis (1971) and Lewis (1974)25See: Field (1977), particulary pg. 381-383 and pg. 401-40226Field (1998), pg. 19

53

can only answer the question ‘what does this evidential system entitle one to infer,’ if one

can employ deductive logic; and really, one can only assent to some evidential system and

infer certain beliefs or conclusions if they can employ deductive logic.

Exactly what standing this gives deductive logic, however, is still unclear. Earlier it

was mentioned that if one were to ask ‘why is it reasonable to use modus ponens?,’ the

non-factualist would re-frame the question: “why value a methodology that allows the use

of modus ponens?” This suggests that some deductive inferential rule is itself a part of

the evidential system. So, the idea would be that deductive logic is ‘indispensable’ to the

extent that some certain principles, some notion of entailment,27 must be explicitly invoked

in any evidential system one assents to.

For example, there may be some evidential system, I , which entitles one to a set of

particular conclusions, C . But, C would not be determined by those principles in I , unless,

at least, among those principles assumed is a deductive system, D , which will contain a

notion of entailment and a set of logical connectives.

Then, there appears to be two rule-circular justifications. The first is within evidential

systems. Since those evidential systems assume some deductive principles, any conclusions

we draw from those systems we assent to are to be explained in terms of the rules as-

sumed. The second rule-circular justification happens at the more general level of goals

and inductive confidence levels about evidential systems. Here, because our inductions are

immodest, they too rule-circularly explain how we come to have the confidence level and

confidence threshold which determines which evidential system we will prefer.28 There is

27Here I use the language of David Ripley (See, Ripley (2015)) who suggests that we may give differ-ent semantic readings of the turnstile, which subsequently include meta-logical properties (for example,transitivity, or distributivity).

28One might wonder how one is supposed to reason inductively given a set of rules derived from proba-bilistic axioms—especially if we are capable of changing our inductive methods, or in the case that thesemethods are not biologically innate (both discussions Field takes up and seems to imply are the case).Would this not implicate a background and necessary use of deductive reasoning? The application ofwhatever axioms of probability is, essentially, application of axioms; and any application of axioms isfundamentally a deductive logical practice.

So while, the inductive rules are “immodest” and their ever increasing probabiities are rule-circularjustifications, they are derivative of axioms, and to get to that step we will have to apply some deductivesystem. This has two potential implications. First, it may be the case that there is actually three rule-circular justifications: (A) of conclusions from evidential systems; (B) of our selection of evidential systemsby inductive rules; and (C) of those inductive rules derived from our implicit and truly indispensable

54

a great deal more discussion that could be had about this, but I will focus on just one

aspect here; namely, that it gives us some way of understanding what the other conceptual

obstacle we began with really was.

The problem with saying we might overturn classical logic for the use of some non-

classical logic, is that it is quite difficult to see what impact these other logics would have

on our inductive methods. If we only accept quantum logic when dealing with quantum

phenomena, but our inductive methods stay the same because our implicit deductive sys-

tem, which gives us those inductive rules, is unchanged; then, we might find very high

success with the evidential system that assumes quantum logic, but this system will not

transfer to other domains. But then, it would seem, that we have not overturned anything

about classical logic, since we are still using it to make our judgments about the evidential

systems. If instead our implicit deductive system were to change to quantum logic however,

then it is difficult to see how we might derive our inductive rules, and so how we might

select evidential systems at all. In effect, the worry then is that distributivity may be

necessary to pick evidential systems (or, at least, measure and compare them inductively),

but note that this will not ever be empirically overturned—the restriction is our conceptual

inability to find good inductive rules from non-distributive deductions.

Then, to summarize Field’s non-factualism...

Logical concepts are properly a priori concepts—they are plausible without

empirical evidence and empirically indefeasible. Our evidential systems license

us to infer according to those logical concepts when they are assumed in the

system so used; however, there does not appear to be any set of evidential sys-

tems which would not employ logical concepts (though, exactly which concepts

may be up for debate and revision according to our epistemic goals). So, logic is

‘indispensable’ (or, ‘necessary’) to our epistemic practices. However, to further

move from simply our entitlement under an evidential system to the justifica-

deductive system. This, however, would return one to a view which, along the lines of Hale, wouldindicate a minimal inference kit necessary to doing some derivations of a kind. And, as noted previously,this is explicitly not the view Field wants to argue for, even though it may be the argument he must make.However, whether or not the ‘induction only’ approach forwarded in Field’s probabilistic semantics is rightor not, it does not disturb the minimal point made here—that there is a deductive rule-circular argumentfor the consequences of our evidential systems.

55

tion of our logical conclusions, we must appeal to the rule-circular argument of

those principles. There is no constraint, metaphysically or otherwise, on which

goals we may have (and so which evidential systems we assent to), but our

being inductive reasoners to begin with gives some basis for which we may see

some systems as better or worse.

The next section will return to our three guiding issues: how might non-factualism help

us with Tonk, the type-2 skeptic, or the type-1 skeptic? And, with respect to the lessons

of section 2.4, are we making progress by moving to non-factualism?

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3.4 The Ups and Downs of Non-Factualism

As is now tradition: let’s begin with Tonk. It might immediately seem that non-factualism

raises more concerns about ‘bad connectives’ than it quells. Evidential systems entitle

our logical conclusions according to those logical concepts and principles assumed in the

evidential system; and so, if one assents to an evidential system which involves Tonk,

then they are entitled to their Tonk inferences. Without some further consideration, like

soundness or ‘meaning constitution,’ then any principle can be assumed in the evidential

system, and this is precisely the ‘moderate relativism’ non-factualism results in.

Yet, this line of reasoning is not quite right. One must keep in mind that Field’s

epistemology describes us as fundamentally probabilistic reasoners. Science was explained

as being better than tasseography not because it says it does better (since all evidential

systems do this), but because it does do better; and so, the further implicit point is,

one will recognize that it does better and likely choose to employ ‘science’ (assent to the

relevant ‘science-evidential systems’) over tea leaf reading. This might eventually help us

ward away connectives like Tonk, for they certainly would ‘lose out’ to connectives like

the conditional over time, but note that this does not actually stop one from using Tonk.

Argumentatively, the premise that we are fundamentally inductive reasoners does a fair

bit of ‘heavy lifting’ for Field, but without rules regarding ‘confidence thresholds’ and at

what point one may no longer reasonably assume some principle then Tonk is still on the

table, no matter how badly it performs.

The non-factualist, however, would not mind this conclusion. As we saw earlier,

Field would be happy to call such systems “lousy” and to try and dissuade someone from

employing those logical connectives—certainly this is the thrust behind taking there to be

no fact of the matter about what is reasonable29—but this raises some concerns which I

contest the non-factualist cannot adequately address: particularly, there appears to be a

lack of common ground for which one might try to dissuade someone else, and this answer

29Though expressed implicitly throughout, Field does explicitly say: “Indeed, a main virtue of evalu-ativism is that it removes the force of most sceptical arguments. Most sceptical arguments depend onassuming that reasonableness is a factual property of beliefs or of rules, and on the understandable resis-tance to stripping away the normative nature of reasonableness by identifying it with a natural propertylike reliability.” (Field (2000), pg. 143

57

appears to undermine the indispensability of deductive logic.

In appealing to our being inductive reasoners, Field does not establish some set of prin-

cipled criteria according to which we may rightfully evaluate someone’s evidential system

as permissible or not; but the hope of the claim is that we can establish common ground

on which we can compare our dispositions about evidential systems: ‘look, this system is

not doing so well empirically, but this other system is. Here is my confidence level about

these assumptions. Is yours the same? What epistemic value do you have that would allow

a lower confidence level?’ Of course, this understanding of common ground raises many

more questions and concerns. I will not attempt to discuss this thoroughly, but instead

raise one particularly troubling response.

While Field’s earlier work attempted to supply an explicit set of probabilistic axioms

that we use, his later essays admit that there can be variety not only with respect to

deductive practices and evidential systems, but also inductive practices.30 Furthermore,

to reiterate a point from earlier, it is not clear what inductive reasoning people actually

employ. The non-factualist creates an idealization of someone when they evaluate their

inferences; and so, it would seem, there is very little common ground at all—one does not

know what actual inductive reasoning someone else is using, and those methods need not

be relevantly similar (besides that they are statistical or probabilistic in some manner)

to anyone else’s.31 The idea that we might compare confidence values, for example, to

30Some form of inductive reasoning is indispensable, this Field consistently holds throughout, but thereis admittance of different inductive ‘rules.’ When discussing the circularity of evidential systems and the“immodest” nature of inductive rules generally, Field notes: “For instance, the respective users of twoinductive rules A and B that differ only in the value of a ‘caution parameter’ can agree that Rule A ismore reliable but less powerful than Rule B.” (Field (2000), pg. 143) However, the choice here to differonly by their ‘caution parameter’ is not principled but to continue to make a point about the sorts ofdifferences Field finds reasonable, i.e. inductive rules A and B can differ drastically.

31For those readers who might doubt the immediate possibility that people fail to reason ideally aboutstatistics, see: Tversky and Kahneman (1981). In these well-regarded studies, participants consistently failto reason appropriately according to basic probabilities (and logical conjunction). I would also forward,amusingly, this description from Carroll’s Alice in Wonderland :

As she said these words her foot slipped, and in another moment, splash! she was up to herchin in salt-water. Her first idea was that she had somehow fallen into the sea, ‘and in thatcase I can go back by railway,’ she said to herself. (Alice had been to the seaside once in herlife, and had come to the general conclusion that, wherever you go to on the English coast,you find a number of bathing-machines in the sea, some children digging in the sand withwooden spades, then a row of lodging-houses, and behind them a railway-station.)Carroll

58

show that someone values power and another values reliability depends on the underlying

statistical methods being similar enough in the first place.

Regarding the ‘moderate relativism’ of Tonk, the second issue pointed to was the effect

that this may have on understanding deductive reasoning to be indispensable. Field is very

loose in his characterization of the necessity of deductive inference—recall, we cannot tell

what conclusions one is entitled to given an evidential system without some deductive

reasoning—and minimally all this might call for is some way of ‘reading’ the turnstile

plus a logical connective; but this would have the discomforting consequence that if logic

is indispensable at all, then Tonk is an equal contender to the conditional in principle.

Perhaps the non-factualist would accept this conclusion with open arms—it is, of course,

just a part of moderate relativism and the evaluation of systems—but, with a connective

as dysfunctional as Tonk, it is unclear how one can tell what conclusions are licensed by

an evidential system in the first place. If we use a deductive system that includes Tonk

to make inferences about certain circumstances, our conclusions might be anything at all.

And we have strong reason for believing that such a system will be unlikely to satisfy

any reasonable goals, because it will lead us, whenever we actually infer using the tonk

rules, to believing in entirely unprincipled ways. So, we have a strong case for supposing

that Tonk is going to be part of worse evidential systems, barring really bizarre goals.

What is evident, however, is that the non-factualist lacks the argumentative tools needed

to ‘totally’ stop one from using Tonk.32 What about the type-2 skeptic?

In discussion with the skeptic of logical force, the non-factualist performs excellently:

evidential systems share aspects with both the sort of extreme rule-circular arguments

we saw with Boghossian initially (because they lack a constraint like the rule in question

in being first ‘meaning-constituting’) and the principle of acceptance as understanding

from Hale. One must first assent to the evidential system in question, which then de-

termines what inferences are possible and by what principles; and so to question some

logical conclusion from within an evidential system is to effectively ‘misunderstand’ what

one accepted in the first place. Every evidential system has those rule-circular arguments

(2011), pg. 18

Of course, Alice’s poor inferential behaviour is not itself evidence against the logical structure of thought,but it does familiarly expose the ease of inductive error.

32I leave it up to the reader to decide if this is a better or worse conclusion than the other views discussed.

59

composed of its principles available to it. Before moving on, however, one might recognize

that this is a very different sort of rule-circular justification than those encountered previ-

ously. Particularly, those rules so justified are not justified always, but only with respect

to the evidential system first assented to; and, unlike conceptual roles on Boghossian’s

account, evidential systems do not necessarily provide some semantics or meaning for the

connectives employed.

These features will come back again in chapter four, but it can be said here that there

is a way of employing rule-circular justification which will not depend on some semantics

for the logical connectives beyond their introduction and elimination rules, and which

depends on logical application—one has to first take up some evidential system to employ

in the world for their rule-circular justification—qualities which I will argue are helpful in

answering our three issues. Now we may move on to the type-1 skeptic, noting that Field

does address Carroll’s Tortoise.

Discussion of the type-1 skeptic, unfortunately, has effectively the same features as

the discussion of Tonk (and there is a sense in which the skeptic’s challenge here might be

rephrased: ‘I accept this evidential system with Tonk. Why should I accept your system

with the conditional?’). The non-factualist does not provide any grounds on which to say

that some evidential system must be used or some other other evidential system must

not be used; and so, all that is available to convince the type-1 skeptic is the notion of

‘success’ and any epistemic values they might otherwise have (reliability, power, and so on).

That some system, and so some implicated rule, is successfull and so epistemically useful.

In other words, we attempt to convince them on the basis of the background inductive

reasoning; but, it was shown that little common ground is available when appealing to

inductive reasoning, and one is, in principle, unable to convince the skeptic. Again, Field

does not find this to be a problem, it is simply the consequence of non-factualism.

I propose that there are two fronts on which the non-factualist may attempt to salvage

modus ponens from the skeptic. The first is to argue for it’s being default reasonable,

and the second, which Field acknowledges, is to move to the meta-argument about which

epistemic goals are the right goals to have. Is there any hope for saying that since logic is

a properly a priori concept, that we might be forced to accept modus ponens?

Given that the ‘indispensability’ of logic on Field’s account was so liberally understood,

60

it would seem the answer is ‘no.’ Tonk might not be plausible ‘without empirical evidence,’

and modus ponens might, but there are at least three issues with thinking this will resolve

the skeptic’s doubt. First, sometimes Tonk will lead from accepted premises to true con-

clusions. So, even if the connective is not default reasonable, luck might have it that it is

a posteriori reasonable. Of course, this would only last for a short while (since inevitably

Tonk arguments will chalk up more false conclusions than true ones), but nonetheless it is

a possibility—and more importantly, a possibility the non-factualist allows.

Second, evidential systems aren’t constrained to containing only those notions which

are reasonable, or even only a priori concepts. Indeed, evidential systems are so broadly

construed that they contain our inductive reasoning, some deductive reasoning (which

allows us to understand what entailments are licensed in the system), certain premises

or theoretical laws, and presumably some explicit or implicit inclusion of an individual’s

epistemic goals. Consequently, ‘people usually tell the truth’ is as justifed as modus ponens,

insofar as it is assumed in an evidential system one employs; and so, the conditional might

very well be default reasonable while Tonk is not, but it would appear that no one is

forced to assent to the use of modus ponens if they reject the evidential system. And

third, there is a sense in which it is actually quite difficult to say that Tonk is not default

reasonable: certainly, disjunction introduction and conjunction elimination are default-

reasonable. What then is needed is some specification of a quality that these rules have

together that would not be default reasonable, and this a little more difficult to find.33

Field’s strongest line of argument on this front would be to say that Tonk neither

plausibly describes the world without empirical evidence, nor plausibly tells one what

follows from what. So, when discussing the indispensability of deductive logic, we appealed

to the question: “what does this evidential system entitle us to infer?” Though Tonk does,

in the most literal sense, answer this question (one is entitled to any conclusion), one

might contest that this is not ‘default reasonable.’ However, the moderate relativism non-

factualism leads us to would show that this is really an argument about goals—can the

goals which call for the Tonk connective in the evidential system be shown to be bad?

And so, to shift to the meta-argument about goals (‘one ought to accept this epistemic

33Of course, many have attempted to find such an idea. Earlier, for example, we saw Hale forwardthe criterion of soundness, but this subsequently raised epistemological issues about undoubtability and‘rational insight.’

61

value’), there may be some route to common ground with the skeptic; at least, Field takes

this to be a possibility: “If it’s a moral ought that’s at issue, fine: I’m not opposing moral

standards on which one ought to aim for the truth.”34 Unfortunately, finding such a moral

force is far beyond this thesis and, arguably, the epistemology of logic. It is difficult, at

least, to see how Tonk or the conditional operator have any quality of morality independent

of our use or further considerations. And if one attempts to find some epistemological ought

to constrain the construction of evidential systems, then Field concludes one has committed

a category mistake, for “on the usual understanding of ‘epistemological oughts’ they govern

beliefs, not goals, and I have no idea what the sort of epistemological ought that governs

goals could amount to.”35 It would seem the skeptic wins again.36

There is one positive thing to take away from this ‘category’ answer though: the idea

that there may be more than one kind of thing in play. Earlier in the chapter it was

mentioned that Field used ‘epistemic goal’ as a type of catch-all for varying parts of our

34Field (2000), pg. 141-14235Field (2000), pg. 14236It may be the case that there are other kinds of goals to consider—namely, pragmatic ones—and that

it is too quick to close the book on this issue here. (My thanks to Nick Ray for making this line of reasoningapparent to me, and with great clarity). Unfortunately, I do not have the space to expand in detail onthis matter, but a few brief remarks might be made. First, the ‘pragmatic ought’ could be formulated so:“given one’s stated goals, then one ought to choose, or ought not to choose, some evidential system, e.”Then, the epistemological oughts would govern what one should believe given an evidential system, themoral oughts would govern what goals one should take to be important, and the pragmatic oughts wouldgovern what evidential system one picks to match their goals and so, consequently, constrain their beliefs.Interestingly, this could be read implicitly in Field’s discussion.

The moral ought governing one’s seeking truth might refer to a truth-related goal, but it might also referto one’s selection of systems given other goals. We can see, for example, how ‘reliability’ questionably playsboth roles: reliability might be a goal we just have, but it might also be a goal we have when choosing oursystem (that our system is reliable for, or relative to, those other goals). Since Field supplies no reason tobelieve that reliability is a ‘must-have’ goal, we then might call into question that pragmatic ought whichwould select those systems which ‘match’ our goals. It is, of course, seemingly non-sensical to claim certaingoals and then, by some invoked pragmatic ought which does not involve something like reliability, chooseevidential systems which do not get one closer to satisfying those goals; but, Field’s presented dichotomy ofoughts allows exactly this line of reasoning. Furthermore, this raises an interesting explanatory question:if there was a common pragmatic ought for us to select that system which ‘worked’ for our goals (say,reliability) and this turned out to always mean selecting systems which involved some particular logicalconnectives or concepts—always pick systems with universal quantification and the conditional, say—thenone might wonder what explains the consistent usefulness of those connectives or concepts. There would bea hint of something ‘miraculous,’ as Eugene Wigner found the applicability of mathematics in the physicalworld to be, about those logical concepts implicated (See: Wigner (1990)).

62

evidential systems and practice. There, the distinction between epistemic domains and

epistemic values was introduced. Non-factualism of the sort Field presents is incapable

of answering the type-1 skeptic, or barring the use of Tonk, because there is no common

ground on which comparisons may be made for evidential systems, and this can be suc-

cinctly described by the inability to find an epistemic ought which would constrain goals;

however, it is less clear that we might not find an epistemic ought which might constrain

domains or values. In the next chapter, I will present an amended non-factualism based

on this distinction between epistemic goals and the discussions from our previous chapters.

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Chapter 4

Non-Factualism+ : An Amendment

Non-factualism as presented in the last chapter seemed to fall prey to the lack of common

ground; an issue that we also saw Boghossian’s conceptual role semantics face in chapter

one. Boghossian went so far as to name a principle, (UAR),1 and then, surprisingly, reject

it. For conceptual role semantics, it was impossible to ever persuade a type-1 skeptic with

logic. On the other hand, Field attempts to avoid this dramatic conclusion by presenting

the olive branch that epistemic promiscuity does not lead to a growing population of

radical thinkers; and quoting Richard Jeffrey on the matter: “The fact that it is legal to

wear chain mail in city buses has not filled them with clanking multitudes.”2 Were skeptics

everyday commuters this might suffice, but what is called for here is either a great deal

of patience for the diversity of evidential systems (for those which contain Tonk and those

which do not contain modus ponens) or some shared arena by which to compare systems

and make progress; else, Field, like Boghossian, will have to admit the impotence of logical

persuasion. However, while Boghossian was forced to reject (UAR), it is not clear that

the non-factualist is forced to reject the principled possibility of common ground. Field

uses the notion of an epistemic goal to capture the vast majority of concepts, properties,

and principles of evidential systems, but I argue that this misses a distinction between

epistemic domains and epistemic values—a distinction which will carry the potential for

non-universal common ground.

1Recall, UAR: If something is a genuine reason for believing that p, then,... its rationalizing force oughtto be accessible from any epistemic standpoint.

2Jeffrey (1983), pg. 145

64

First, to reiterate the distinction: I take epistemic domains to determine the boundaries

of what one wants to know, or know about; and I take epistemic values to determine those

qualities one is interested in their evidential system possessing (again, like reliability or

power). Epistemic values can broadly be described as dispositions one has in their inquiry.

And here we might see that Field’s concerns and points are apt: it is difficult to see

how we might have an ‘epistemological ought’ for dispositions; that to argue about one’s

dispositions is likely a moral ought; that even without some metaphysical constraints we

can still evaluate each other’s dispositions even when these evaluations are idealizations

(though this evaluation will be moral not epistemological); that there is no fact of the

matter about what reasonable dispositions there are to have or not; that every evidential

system will be relative to our dispositions; and so on.

In other words, Field’s attempt to describe ‘epistemic goals’ was really to describe

epistemic values. It is not clear that all of the same things can be said about epistemic

domains. Particularly, I argue that epistemic domains are not relative decisions—they can-

not change from person to person—and that epistemic domains have a different conceptual

relation to epistemic oughts than, at least, epistemic values.

Epistemic oughts, Field notes, would have to determine ‘what one believes’ rather

than (in the case of moral oughts) ‘what one’s goals should be.’ However, one might recall,

evidential systems are defined as “a bunch of rules governing what to believe in what

circumstances.”3 It would seem then, that epistemological oughts are not so inconceivable,

rather they are the evidential systems we adopt. Once adopted we are ‘stuck’ with only

those inferential rules available to the system, entitled only to those conclusions made by

applying those rules, and justified in doing so for as long as the evidential system remains

accepted.

It is imperative to carve out which components are actually necessary to an evidential

system, so that it may be clear what one ought to believe and why.4 Given Field’s de-

scription, an evidential system is seemingly composed of five parts, but I will contest that

only one is actually necessary in any significant sense. Furthermore, there also appears

to be the mistake of assuming that all of these parts are component within the evidential

3Field (1996), pg. 3624Something Field unfortunately neglected to explicitly do.

65

system, rather than being invoked in all situations, but not as a part of the system. So,

an evidential system on Field’s account contains:

1: A method of inductive reasoning

– Bayesian statistics, a set of probabilistic axioms and derived functions, etc.

2: Any related epistemic values

– Simplicity, Reliability, Power, etc.

3: Claims taken for granted

– A set of statements that have a definite truth value (i.e. the laws of physics)

4: A deductive system

– A reading of the turnstile and set of connectives

5: An epistemic domain

– A universe of discourse

All according to the non-factualist: We are fundamentally probabilistic reasoners, so a

method of inductive reasoning will always be necessitated, even if in all cases it is ‘merely’

that method fundamental to us. (Though, note, this does not commit one to a univer-

sal method, only the presence of a method). The deductive system and those claims we

take for granted determine the possible conclusions we are entitled to inferentially; and

without this deductive capacity we could not know what our system licensed. And finally,

epistemic values and the epistemic domain set ‘the agenda:’ what do we want to know

about, and what qualities is one interested in satisfying? However, I will presently at-

tempt to show—considering each item in order—this picture of the evidential system to

be problematic.

First, it does not appear that inductive reasoning is necessarily within the the evidential

system. It might be the case that the circumstances seem to call for some inductive method

to be specified, in which case there certainly will be some inductive reasoning component,

but this need not always be the case. Inductive reasoning is best described, in the spirit

66

of Field’s position, as a tool we fundamentally use to make sense of evidential systems

generally. It is how we compare systems—more confidence in this one than that one.

Furthermore, and more importantly, two people can have competing inductive methods

and still make sense of the fact that they are comparing like systems. So, except in

some very special cases, or when attempting to compare results according to the inductive

methods invoked, one is free to choose their preferred inductive reasoning, if any at all,

according to their goals.

Similarly, for the second category of epistemic values, it is a stretch to see these as

principles within an evidential system. When one assents to an evidential system they

are doing so according to their epistemic goals, which we established to be, if not contain,

epistemic values. Two people can have competing epistemic values and still make sense of

the fact that they are comparing like systems.

The third part concerns those propositions we take to be axioms. Here one might

think of ‘the laws of physics.’ Principles of this sort appear to fit better within an evi-

dential system (at least, it is not clear that these axioms are part of our epistemic goals),

they determine what are permissible or impermissible things to deduce in the evidential

system—if one takes for granted that p, then assuming they also employ, say, the law of

non-contradiction, that evidential system would never entitle one to ¬p. Note, however,

neither must one take anything for granted when they assent to an evidential system nor

must they take the same claims for granted as someone else—certainly, ‘the laws of physics’

are not settled. So, it would seem, axiomatic claims are parts that rightfully belong in ev-

idential systems but are not necessary. There may be disagreement between two people

about which claims to take for granted, and yet still compare their systems; one is, again,

free to choose.

The fourth part is something we certainly see as part of the evidential system:5 without

a deductive system we cannot begin to make sense of what our evidential system will

5There is the further discussion, brought up previously, about the difficulty in squaring the derivationof inductive rules without a deductive system, but this point can again be left to the side. For even ifit were the case that some deductive system was implicit for us globally and ‘necessary’ in this sense, itdoes not follow that the deductive systems employed within evidential systems would have to match thatfundamental one we already possess. This would, of course, undermine the whole project laid out andraise all manner of concerns seen in Chapter 2 about how we come to know those principles involved inthe ‘indispensable kit.’

67

determine. But, again, one might note that there can be disagreement here: one is free to

choose which deductive system they prefer. This is precisely what the type-1 skeptic does,

for example.

This leaves the final component: epistemic domains. Understanding these domains as

our universe of discourse should help to make it apparent how they differ from the other

parts. For starters, they do not immediately seem to be contained by evidential systems:

they are neither the circumstances in the world, nor are they a rule we infer by; rather, they

set the boundaries of what an evidential system is about. And here we may now see how

they stand apart from all the other components as well; if two people differ in their universe

of discourse then it is difficult to see how they might compare results at all. Every other

choice may be cashed out in terms of what epistemic goals one has (or more particularly,

epistemic values if we assume the only epistemic goals are values and domains), but if one

changes their universe of discourse then no comparison is possible—the two systems are

being applied to different domains.6 There are inevitably some special cases to such an

idea,7 but if it can be said that at least the epistemic domains of two systems must be the

same for one to compare them, then we can begin to make progress.

So, our evidential systems are not made of five components but instead contain: three

6It is tempting to say ‘applied to different circumstances’ here, but one must be careful to distinguishbetween those circumstances which are actual, and which may be captured, or not, by the ‘domain,’ whichis rather the conceptual boundaries one sets up for possible circumstances.

7Particularly, there are three cases I can immediately spot. The first is when the universe of discourse forone evidential system contains the universe of discourse of the other system, i.e. when one system is morebroad than the other. One might be temped to say that here an epistemic value about reliability or powerwould come into play, but this would subsume epistemic domains under epistemic values—would meanthat the epistemic domains as goals depend upon our epistemic values. Instead, since we are attemptingto fix the domains, any evaluations according to our epistemic values should be of the consequences of theevidential system or our inductive reasoning about the evidential systems but not the domain itself. So, ifone epistemic domain contains another, this means nothing more than if you had two epistemic domainswho had no common elements. Different domains, different systems.

The second and third are the cases where the universe of discourse is ‘full’ and empty. Taking ‘full’to mean something along the lines of, ‘the universe of discourse which specifies exactly all things to inferabout,’ I can only conclude that the systems involved and so compared would be so radically different, andthat there would be so many to compare, that one would have to concede a ‘not-so moderate relativism’of the sort faced in chapter three. However, to even begin entertaining this hypothetical brings to the forewell-trodden paradoxes—for instance, a set of all sets. And in the case of the empty universe of discourse,I would argue that there is no application at all, and so no comparison to be made. What would it meanto apply an evidential system to nothing?

68

functional parts, one set of principles the system is contingent upon, and a ‘domain of

applicability’. There is the necessary deductive system, and the unnecessary (in that they

may permissibly be ‘empty’ or otherwise non-existent) axioms and inductive reasoning.

Each of these three parts may be changed freely. There is the set of epistemic values, one

of the sets of principles, which are relative to the individual who is selecting the evidential

system. And finally, there is the epistemic domain which specifies exactly what the system

is allowed to be applied to. This make-up of the evidential system will allow us to address

the skeptic, but first the notion of applicability will have to be unpacked, since, evidently,

a lot rides on it.

In the last lesson of section 2.4, it was noted that we should consider the introduction

and elimination rules as a sufficient semantics for the connectives, and that Russell’s asser-

tion and reference distinction might help us understand how assent functions with logical

statements. There are those logical schema which we can reference in abstract but when

we go to assert them in the world we are doing something quite different. Regarding this

difference, Russell says:

“It is plain that, if I may be allowed to use the word assertion in a non-

psychological sense, the proposition ‘p implies q’ asserts an implication, though

it does not assert p or q. The p and the q which enter into this proposition are

not strictly the same as the p or the q which are separate propositions, at least,

if they are true.”8

Russell then advocates for a purely logical notion of ‘therefore,’ which would solve the

subsequent issue of how unasserted propositions can justify asserted propositions (answer,

in effect, Carroll’s Tortoise); but what I would suggest here is that there is an epistemic

(though not necessarily psychological) way of cashing out assertion and reference. When

we take on board an evidential system and a universe of discourse, we are implicitly making

a further claim about the deductive systems we employ; namely, that they apply to the

world—that some p→ q statement actually maps on to those phenomena in the universe of

discourse we are concerned with. Subsequently, when thinking in non-factualist terms, rule-

circular justifications are not for the rule ‘in abstract,’ but for the rule’s application to the

8Russell (2009), §38

69

circumstances; and this better explains why the rules we provide rule-circular justification

for ‘are not justified always,’ for they are domain relative. The justifcations are not just

contingent to the evidential systems in a broad sense, but also to the particulars of the

universe of discourse; and these particulars provide feedback in the form of our conlusions

being true or false—our mapping of actual worldly relationships into logical ones being apt

or not.

Now, regarding our guiding issues, we may see how these amendments fare. The type-2

skeptic was handled to begin with, so no further commentary is needed there, but non-

factualism still needs some way of addressing Tonk and the type-1 skeptic. Given that

we know Tonk to be at least principally permissible, I will run the two issues together

in this conclusion for convenience: how do you convince someone who uses Tonk, to use

the conditional? The moderate relativism of Field’s non-factualism meant there was no

non-moralistic argument against one who uses Tonk because there was no common-ground,

no way of appealing to some shared inductive reasoning or, obviously, deductive system,

to show them why using Tonk is a bad idea. However, by fixing the universe of discourse

over time, it is possible to ‘count the truths’ in a straightforward manner. One need not

appeal to inductive confidence values or to epistemic values about power or reliability, for

there is an emergent ratio of true conclusions to untrue concusions for each system. This

has a number of consequences, but here I will note two which I see to be pertinent.

First, as noted in chapter three, if there is no principle behind what the standing of

some evidential system need be for it to be reasonably employed (a particular confidence

level or probability, etc.) then it is diffcult to see how ‘counting the truths’ can help. True

though that may be, there are many ways of understanding what ‘better’ means; and on

this account, once the domain has been fixed, there is the undeniable common ground that

one evidential system has more truths than another (or not), within that domain. Perhaps

that would not stop a skeptic entirely from refusing to switch systems—they may insist on

trying out more and more different evidential systems with the same universe of discourse,

or insisting on a different standard of ‘better’ (a different threshold)—but where we were

entirely lost before, we have now found one footing. Non-factualism is looking to the long

run to show that some evidential system is better. Unless we invoke a new type-3 skeptic,

who will say that truths do not count positively towards an evidential system, then it

70

would seem that we have cornered off one of the type-1 skeptic’s escape routes.

Second, one might think that the type-1 skeptic has the potential to retreat to a

different universe of discourse, but this would fail for two reasons. (1) It is precisely by

fixing the universe of discourse that we have the potential for common ground—if we are

to move to another universe of discourse, then fine; Tonk will likely do no better and we

are right back where we started, counting truths in a different domain. (2) If somehow

there was a universe of discourse where Tonk did resoundingly well and the conditional

failed, this would not count against any other system which posits a different universe of

discourse, for there is no sense in which one is now comparing like systems. If such a

myserious domain were found, then the type-1 skeptic would better be understood as the

individual who refuses to assent to Tonk and argues instead for the conditional. In effect,

the position here is not arguing for the conditional directly—though, I take the liberty

of assuming that this argument is an arugment in favour of the conditional—but instead,

for those connectives which ‘fit’ the domain best: quantum logic for quantum phenomena,

classical logical for classical phenomena, and tonk-logic for tonk-phenomena.

Here I have tried to advance the non-factualist approach to answering the logical

skeptics, even if only minimally. I have not eliminated all doubts, but instead limited

those available doubts the skeptics have. Unless one is going to argue that truth has no

bearing on one evidential system being better, then there both is a route to common ground

among evidential systems and a persuasive force.

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Chapter 5

Conclusion

We began with three simple problems: the nagging bad company of logical connectives

which seem well-specified, but which trivialize our endeavours; the Tortoise who claimed

to agree with our logical concepts but refused to conclude in accordance with them; and

the yet worse skeptic who denied the efficacy of our logical concepts tout court. And

no position considered was capable of answering all three without issue. Here, I have

proposed a modification to non-factualism in the form of a distinction between epistemic

domains and epistemic values, providing common ground on which to address the logical

skeptic. While the amended non-factualist position does not definitively address the issue,

it is largely an epistemically feasible project and the distinction proposed does limit the

argumenative capacities of the skeptic.

72

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